1
|
Basak A, Dana SK, Bairagi N, Feudel U. When do multiple pulses of environmental variation trigger tipping in an ecological system? CHAOS (WOODBURY, N.Y.) 2024; 34:093105. [PMID: 39226474 DOI: 10.1063/5.0205410] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/26/2024] [Accepted: 07/29/2024] [Indexed: 09/05/2024]
Abstract
Climate change and anthropogenic impacts have a significant effect on natural ecosystems. As a response, tipping phenomena, i.e., abrupt qualitative changes in the dynamics of ecosystems, like transitions between alternative stable states, can be observed. We study such critical transitions, caused by an interplay between B-tipping, the rate of change of environmental forcing, and a rate-dependent basin boundary crossing. Instead of a slow trend of environmental change, we focus on pulses of variation in the carrying capacity in a simple ecological model, the spruce budworm model, and show how one pulse of environmental change can lead to tracking the current stable state or to tipping to an alternative state depending on the strength and the duration of the pulse. Moreover, we demonstrate that applying a second pulse after the first one, which can track the desired state, can lead to tipping, although its rate is slow and does not even cross the critical threshold. We explain this unexpected behavior in terms of the interacting timescales, the intrinsic ecological timescale, the rate of environmental change, and the movement of the basin boundaries separating the basins of attraction of the two alternative states.
Collapse
Affiliation(s)
- Ayanava Basak
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Nandadulal Bairagi
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University Oldenburg, 26129 Oldenburg, Germany
| |
Collapse
|
2
|
Basak A, Dana SK, Bairagi N. Partial tipping in bistable ecological systems under periodic environmental variability. CHAOS (WOODBURY, N.Y.) 2024; 34:083130. [PMID: 39177960 DOI: 10.1063/5.0215157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2024] [Accepted: 08/06/2024] [Indexed: 08/24/2024]
Abstract
Periodic environmental variability is a common source affecting ecosystems and regulating their dynamics. This paper investigates the effects of periodic variation in species growth rate on the population dynamics of three bistable ecological systems. The first is a one-dimensional insect population model with coexisting outbreak and refuge equilibrium states, the second one describes two-species predator-prey interactions with extinction and coexistence states, and the third one is a three-species food chain model where chaotic and limit cycle states may coexist. We demonstrate with numerical simulations that a periodic variation in species growth rate may cause switching between two coexisting attractors without crossing any bifurcation point. Such a switchover occurs only for a specific initial population density close to the basin boundary, leading to partial tipping if the frozen system is non-chaotic. Partial tipping may also occur for some initial points far from the basin boundary if the frozen system is chaotic. Interestingly, the probability of tipping shows a frequency response with a maximum for a specific frequency of periodic forcing, as noticed for equilibrium and non-equilibrium limit cycle systems. The findings suggest that unexpected outbreaks or abrupt declines in population density may occur due to time-dependent variations in species growth parameters. Depending on the selective frequency of the periodic environmental variation, this may lead to species extinction or help the species to survive.
Collapse
Affiliation(s)
- Ayanava Basak
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Nandadulal Bairagi
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| |
Collapse
|
3
|
Lehnertz K. Time-series-analysis-based detection of critical transitions in real-world non-autonomous systems. CHAOS (WOODBURY, N.Y.) 2024; 34:072102. [PMID: 38985967 DOI: 10.1063/5.0214733] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2024] [Accepted: 06/21/2024] [Indexed: 07/12/2024]
Abstract
Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very different and, at times, even disastrous dynamical regimes. Since such critical transitions disrupt the systems' intended or desired functionality, it is crucial to understand the underlying mechanisms, to identify precursors of such transitions, and to reliably detect them in time series of suitable system observables to enable forecasts. This review critically assesses the various steps of investigation involved in time-series-analysis-based detection of critical transitions in real-world non-autonomous systems: from the data recording to evaluating the reliability of offline and online detections. It will highlight pros and cons to stimulate further developments, which would be necessary to advance understanding and forecasting nonlinear behavior such as critical transitions in complex systems.
Collapse
|
4
|
Bergeot B, Terrien S, Vergez C. Predicting transient dynamics in a model of reed musical instrument with slowly time-varying control parameter. CHAOS (WOODBURY, N.Y.) 2024; 34:073146. [PMID: 39042504 DOI: 10.1063/5.0190512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Accepted: 07/05/2024] [Indexed: 07/25/2024]
Abstract
When playing a self-sustained reed instrument (such as the clarinet), initial acoustical transients (at the beginning of a note) are known to be of crucial importance. Nevertheless, they have been mostly overlooked in the literature on musical instruments. We investigate here the dynamic behavior of a simple model of reed instrument with a time-varying blowing pressure accounting for attack transients performed by the musician. In practice, this means studying a one-dimensional non-autonomous dynamical system obtained by slowly varying in time the bifurcation parameter (the blowing pressure) of the corresponding autonomous systems, i.e., whose bifurcation parameter is constant. In this context, the study focuses on the case for which the time-varying blowing pressure crosses the bistability domain (with the coexistence of a periodic solution and an equilibrium) of the corresponding autonomous model. Considering the time-varying blowing pressure as a new (slow) state variable, the considered non-autonomous one-dimensional system becomes an autonomous two-dimensional fast-slow system. In the bistability domain, the latter has attracting manifolds associated with two stable branches of the bifurcation diagram of the system with constant parameter. In the framework of the geometric singular perturbation theory, we show that a single solution of the two-dimensional fast-slow system can be used to describe the global system behavior. Indeed, this allows us to determine, depending on the initial conditions and rate of change of the blowing pressure, which manifold is approached when the bistability domain is crossed and to predict whether a sound is produced during transient as a function of the musician's control.
Collapse
Affiliation(s)
- B Bergeot
- INSA CVL, Univ. Orléans, Univ. Tours, LaMé UR 7494, F-41034, 3 Rue de la Chocolaterie, CS 23410, 41034 Blois Cedex, France
| | - S Terrien
- Laboratoire d'Acoustique de l'Université du Mans (LAUM), UMR 6613, Institut d'Acoustique-Graduate School (IA-GS), CNRS, Le Mans Université, Le Mans, France
| | - C Vergez
- Aix Marseille Univ, CNRS, Centrale Med, LMA UMR 7031, Marseille, France
| |
Collapse
|
5
|
Narayan Chattopadhyay S, Kumar Gupta A. Tipping points, multistability, and stochasticity in a two-dimensional traffic network dynamics. CHAOS (WOODBURY, N.Y.) 2024; 34:073107. [PMID: 38949532 DOI: 10.1063/5.0202785] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/07/2024] [Accepted: 06/08/2024] [Indexed: 07/02/2024]
Abstract
Mitigating traffic jams is a critical step for the betterment of the urban transportation system, which comprises a large number of interconnected routes to form an intricate network. To understand distinct features of vehicular traffic flow on a network, a macroscopic two-dimensional traffic network model is proposed incorporating intra-nodal and inter-nodal vehicular interaction. Utilizing the popular techniques of nonlinear dynamics, we investigate the impact of different parameters like occupancy, entry rates, and exit rates of vehicles. The existence of saddle-node, Hopf, homoclinic, Bogdanov-Takens, and cusp bifurcations have been shown using single or biparametric bifurcation diagrams. The occurrences of different multistability (bistability/tristability) phenomena, stochastic switching, and critical transitions are explored in detail. Further, we calculate the possibility of achieving each alternative state using the basin stability metric to characterize multistability. In addition, critical transitions from free flow to congestion are identified at different magnitudes of stochastic fluctuations. The applicability of critical slowing down based generic indicators, e.g., variance, lag-1 autocorrelation, skewness, kurtosis, and conditional heteroskedasticity are investigated to forewarn the critical transition from free flow to traffic congestion. It is demonstrated through the use of simulated data that not all of the measures exhibit sensitivity to rapid phase transitions in traffic flow. Our study reveals that traffic congestion emerges because of either bifurcation or stochasticity. The result provided in this study may serve as a paradigm to understand the qualitative behavior of traffic jams and to explore the tipping mechanisms occurring in transport phenomena.
Collapse
|
6
|
Junquera V, Schlüter M, Rocha J, Wunderling N, Levin SA, Rubenstein DI, Castella JC, Meyfroidt P. Crop booms as regime shifts. ROYAL SOCIETY OPEN SCIENCE 2024; 11:231571. [PMID: 39100184 PMCID: PMC11296141 DOI: 10.1098/rsos.231571] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/19/2023] [Revised: 03/11/2024] [Accepted: 04/17/2024] [Indexed: 08/06/2024]
Abstract
A crop boom is a sudden, nonlinear and intense expansion of a new crop. Despite their large impacts, boom-bust dynamics are not well understood; booms are largely unpredictable and difficult to steer once they unfold. Based on the striking resemblances between land regime shifts and crop booms, we apply complex systems theory, highlighting the potential for regime shifts, to provide new insights about crop boom dynamics. We analyse qualitative and quantitative data of rubber and banana plantation expansion in two forest frontier regions of northern Laos. We show that preconditions, including previous booms, explain the occurrence (why) of booms, and triggers like policy and market changes explain their timing (when). Yet, the most important features of booms, their intensity and nonlinearity (how), strongly depended on internal self-reinforcing feedbacks. We identify built-in feedbacks (neighbourhood effects and imitation) and emergent feedbacks (land rush) and show that they were social in nature, multi-scale from plot to region and subject to thresholds. We suggest that these are regular features of booms and propose a definition and causal-mechanistic explanation of crop booms, examining the overlap between booms and regime shifts and the role of frontiers. We then identify opportunities for management interventions before, during and after booms.
Collapse
Affiliation(s)
- Victoria Junquera
- High Meadows Environmental Institute, Princeton University, Princeton, NJ, USA
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
| | - Maja Schlüter
- Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden
| | - Juan Rocha
- Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden
| | - Nico Wunderling
- High Meadows Environmental Institute, Princeton University, Princeton, NJ, USA
- FutureLab Earth Resilience in the Anthropocene, Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany
- Center for Critical Computational Studies (C³S), Goethe University Frankfurt, Frankfurt am Main, Germany
| | - Simon A. Levin
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
| | - Daniel I. Rubenstein
- Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, USA
| | | | - Patrick Meyfroidt
- Earth and Life Institute, UCLouvain, Louvain-la-Neuve, Belgium
- F.R.S.-FNRS, Brussels, Belgium
| |
Collapse
|
7
|
Sadhu S, Chakraborty Thakur S. Analysis of long transients and detection of early warning signals of extinction in a class of predator-prey models exhibiting bistable behavior. J Math Biol 2024; 88:70. [PMID: 38668899 DOI: 10.1007/s00285-024-02095-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2023] [Revised: 04/01/2024] [Accepted: 04/09/2024] [Indexed: 05/12/2024]
Abstract
In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the predators. In a parameter regime near a singular zero-Hopf bifurcation of the coexistence equilibrium state, we assume that the system under study exhibits bistability between a periodic attractor that bifurcates from the singular Hopf point and another attractor, which could be a periodic attractor or a point attractor, such that the invariant manifolds of the coexistence equilibrium point play central roles in organizing the dynamics. To find whether a solution that starts in a vicinity of the coexistence equilibrium approaches the periodic attractor or the other attractor, we reduce the equations to a suitable normal form, and examine the basin boundary near the singular Hopf point. A key component of our study includes an analysis of the long transient dynamics, characterized by their rapid oscillations with a slow variation in amplitude, by applying a moving average technique. We obtain a set of necessary and sufficient conditions on the initial values of a solution near the coexistence equilibrium to determine whether it lies in the basin of attraction of the periodic attractor. As a result of our analysis, we devise a method of identifying early warning signals, significantly in advance, of a future crisis that could lead to extinction of one of the predators. The analysis is applied to the predator-prey model considered in Sadhu (Discrete Contin Dyn Syst B 26:5251-5279, 2021) and we find that our theory is in good agreement with the numerical simulations carried out for this model.
Collapse
Affiliation(s)
- S Sadhu
- Department of Mathematics, Georgia College & State University, Milledgeville, GA, 31061, USA.
| | | |
Collapse
|
8
|
Arumugam R, Guichard F, Lutscher F. Early warning indicators capture catastrophic transitions driven by explicit rates of environmental change. Ecology 2024; 105:e4240. [PMID: 38400588 DOI: 10.1002/ecy.4240] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 10/26/2023] [Indexed: 02/25/2024]
Abstract
In response to external changes, ecosystems can undergo catastrophic transitions. Early warning indicators aim to predict such transitions based on the phenomenon of critical slowing down at bifurcation points found under a constant environment. When an explicit rate of environmental change is considered, catastrophic transitions can become distinct phenomena from bifurcations, and result from a delayed response to noncatastrophic bifurcations. We use a trophic metacommunity model where transitions in time series and bifurcations of the system are distinct phenomena. We calculate early warning indicators from the time series of the continually changing system and show that they predict not the bifurcation of the underlying system but the actual catastrophic transition driven by the explicit rate of change. Predictions based on the bifurcation structure could miss catastrophic transitions that can still be captured by early warning signals calculated from time series. Our results expand the repertoire of mechanistic models used to anticipate catastrophic transitions to nonequilibrium ecological systems exposed to a constant rate of environmental change.
Collapse
Affiliation(s)
- Ramesh Arumugam
- Department of Biology, McGill University, Montreal, Quebec, Canada
| | | | - Frithjof Lutscher
- Department of Mathematics and Statistics, and Department of Biology, University of Ottawa, Ottawa, Ontario, Canada
| |
Collapse
|
9
|
Ezraty R, Levin I, Gat O. Universality and hysteresis in slow sweeping of bifurcations. Phys Rev E 2024; 109:044206. [PMID: 38755885 DOI: 10.1103/physreve.109.044206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2023] [Accepted: 03/21/2024] [Indexed: 05/18/2024]
Abstract
Bifurcations in dynamical systems are often studied experimentally and numerically using a slow parameter sweep. Focusing on the cases of period-doubling and pitchfork bifurcations in maps, we show that the adiabatic approximation always breaks down sufficiently close to the bifurcation, so the upsweep and downsweep dynamics diverge from one another, disobeying standard bifurcation theory. Nevertheless, we demonstrate universal upsweep and downsweep trajectories for sufficiently slow sweep rates, revealing that the slow trajectories depend essentially on a structural asymmetry parameter, whose effect is negligible for the stationary dynamics. We obtain explicit asymptotic expressions for the universal trajectories and use them to calculate the area of the hysteresis loop enclosed between the upsweep and downsweep trajectories as a function of the asymmetry parameter and the sweep rate.
Collapse
Affiliation(s)
- Roie Ezraty
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| | - Ido Levin
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Omri Gat
- Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 9190401, Israel
| |
Collapse
|
10
|
Tsubota T, Liu C, Foster B, Knobloch E. Bifurcation delay and front propagation in the real Ginzburg-Landau equation on a time-dependent domain. Phys Rev E 2024; 109:044210. [PMID: 38755931 DOI: 10.1103/physreve.109.044210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2023] [Accepted: 03/12/2024] [Indexed: 05/18/2024]
Abstract
This work analyzes bifurcation delay and front propagation in the one-dimensional real Ginzburg-Landau equation with periodic boundary conditions on isotropically growing or shrinking domains. First, we obtain closed-form expressions for the delay of primary bifurcations on a growing domain and show that the additional domain growth before the appearance of a pattern is independent of the growth time scale. We also quantify primary bifurcation delay on a shrinking domain; in contrast with a growing domain, the time scale of domain compression is reflected in the additional compression before the pattern decays. For secondary bifurcations such as the Eckhaus instability, we obtain a lower bound on the delay of phase slips due to a time-dependent domain. We also construct a heuristic model to classify regimes with arrested phase slips, i.e., phase slips that fail to develop. Then, we study how propagating fronts are influenced by a time-dependent domain. We identify three types of pulled fronts: homogeneous, pattern spreading, and Eckhaus fronts. By following the linear dynamics, we derive expressions for the velocity and profile of homogeneous fronts on a time-dependent domain. We also derive the natural "asymptotic" velocity and front profile and show that these deviate from predictions based on the marginal stability criterion familiar from fixed domain theory. This difference arises because the time dependence of the domain lifts the degeneracy of the spatial eigenvalues associated with speed selection and represents a fundamental distinction from the fixed domain theory that we verify using direct numerical simulations. The effect of a growing domain on pattern spreading and Eckhaus front velocities is inspected qualitatively and found to be similar to that of homogeneous fronts. These more complex fronts can also experience delayed onset. Lastly, we show that dilution-an effect present when the order parameter is conserved-increases bifurcation delay and amplifies changes in the homogeneous front velocity on time-dependent domains. The study provides general insight into the effects of domain growth on pattern onset, pattern transitions, and front propagation in systems across different scientific fields.
Collapse
Affiliation(s)
- Troy Tsubota
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - Chang Liu
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
- School of Mechanical, Aerospace, and Manufacturing Engineering, University of Connecticut, Storrs, Connecticut 06269, USA
| | - Benjamin Foster
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| | - Edgar Knobloch
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
| |
Collapse
|
11
|
Legault V, Pu Y, Weinans E, Cohen AA. Application of early warning signs to physiological contexts: a comparison of multivariate indices in patients on long-term hemodialysis. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 4:1299162. [PMID: 38595863 PMCID: PMC11002238 DOI: 10.3389/fnetp.2024.1299162] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/22/2023] [Accepted: 03/15/2024] [Indexed: 04/11/2024]
Abstract
Early warnings signs (EWSs) can anticipate abrupt changes in system state, known as "critical transitions," by detecting dynamic variations, including increases in variance, autocorrelation (AC), and cross-correlation. Numerous EWSs have been proposed; yet no consensus on which perform best exists. Here, we compared 15 multivariate EWSs in time series of 763 hemodialyzed patients, previously shown to present relevant critical transition dynamics. We calculated five EWSs based on AC, six on variance, one on cross-correlation, and three on AC and variance. We assessed their pairwise correlations, trends before death, and mortality predictive power, alone and in combination. Variance-based EWSs showed stronger correlations (r = 0.663 ± 0.222 vs. 0.170 ± 0.205 for AC-based indices) and a steeper increase before death. Two variance-based EWSs yielded HR95 > 9 (HR95 standing for a scale-invariant metric of hazard ratio), but combining them did not improve the area under the receiver-operating curve (AUC) much compared to using them alone (AUC = 0.798 vs. 0.796 and 0.791). Nevertheless, the AUC reached 0.825 when combining 13 indices. While some indicators did not perform overly well alone, their addition to the best performing EWSs increased the predictive power, suggesting that indices combination captures a broader range of dynamic changes occurring within the system. It is unclear whether this added benefit reflects measurement error of a unified phenomenon or heterogeneity in the nature of signals preceding critical transitions. Finally, the modest predictive performance and weak correlations among some indices call into question their validity, at least in this context.
Collapse
Affiliation(s)
- Véronique Legault
- Research Center of the Centre Hospitalier Universitaire de Sherbrooke, Sherbrooke, QC, Canada
| | - Yi Pu
- PRIMUS Research Group, Department of Family Medicine, University of Sherbrooke, Sherbrooke, QC, Canada
| | - Els Weinans
- Copernicus Institute of Sustainable Development, Environmental Science, Faculty of Geosciences, Utrecht University, Utrecht, Netherlands
| | - Alan A. Cohen
- Research Center of the Centre Hospitalier Universitaire de Sherbrooke, Sherbrooke, QC, Canada
- PRIMUS Research Group, Department of Family Medicine, University of Sherbrooke, Sherbrooke, QC, Canada
| |
Collapse
|
12
|
Lohmann J, Dijkstra HA, Jochum M, Lucarini V, Ditlevsen PD. Multistability and intermediate tipping of the Atlantic Ocean circulation. SCIENCE ADVANCES 2024; 10:eadi4253. [PMID: 38517955 PMCID: PMC10959405 DOI: 10.1126/sciadv.adi4253] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 02/20/2024] [Indexed: 03/24/2024]
Abstract
Tipping points (TP) in climate subsystems are usually thought to occur at a well-defined, critical forcing parameter threshold, via destabilization of the system state by a single, dominant positive feedback. However, coupling to other subsystems, additional feedbacks, and spatial heterogeneity may promote further small-amplitude, abrupt reorganizations of geophysical flows at forcing levels lower than the critical threshold. Using a primitive-equation ocean model, we simulate a collapse of the Atlantic Meridional Overturning Circulation (AMOC) due to increasing glacial melt. Considerably before the collapse, various abrupt, qualitative changes in AMOC variability occur. These intermediate tipping points (ITP) are transitions between multiple stable circulation states. Using 2.75 million years of model simulations, we uncover a very rugged stability landscape featuring parameter regions of up to nine coexisting stable states. The path to an AMOC collapse via a sequence of ITPs depends on the rate of change of the meltwater input. This challenges our ability to predict and define safe limits for TPs.
Collapse
Affiliation(s)
- Johannes Lohmann
- Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Denmark
| | - Henk A Dijkstra
- Institute for Marine and Atmospheric research Utrecht, Utrecht University, Utrecht, Netherlands
| | - Markus Jochum
- Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Denmark
| | - Valerio Lucarini
- Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK
| | - Peter D Ditlevsen
- Physics of Ice, Climate and Earth, Niels Bohr Institute, University of Copenhagen, Denmark
| |
Collapse
|
13
|
Bröhl T, Rings T, Pukropski J, von Wrede R, Lehnertz K. The time-evolving epileptic brain network: concepts, definitions, accomplishments, perspectives. FRONTIERS IN NETWORK PHYSIOLOGY 2024; 3:1338864. [PMID: 38293249 PMCID: PMC10825060 DOI: 10.3389/fnetp.2023.1338864] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2023] [Accepted: 12/19/2023] [Indexed: 02/01/2024]
Abstract
Epilepsy is now considered a network disease that affects the brain across multiple levels of spatial and temporal scales. The paradigm shift from an epileptic focus-a discrete cortical area from which seizures originate-to a widespread epileptic network-spanning lobes and hemispheres-considerably advanced our understanding of epilepsy and continues to influence both research and clinical treatment of this multi-faceted high-impact neurological disorder. The epileptic network, however, is not static but evolves in time which requires novel approaches for an in-depth characterization. In this review, we discuss conceptual basics of network theory and critically examine state-of-the-art recording techniques and analysis tools used to assess and characterize a time-evolving human epileptic brain network. We give an account on current shortcomings and highlight potential developments towards an improved clinical management of epilepsy.
Collapse
Affiliation(s)
- Timo Bröhl
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Jan Pukropski
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Randi von Wrede
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany
- Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
- Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
| |
Collapse
|
14
|
Terpstra S, Marquitti FMD, Vasconcelos VV. Adaptive foraging of pollinators fosters gradual tipping under resource competition and rapid environmental change. PLoS Comput Biol 2024; 20:e1011762. [PMID: 38194414 PMCID: PMC10802948 DOI: 10.1371/journal.pcbi.1011762] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Revised: 01/22/2024] [Accepted: 12/15/2023] [Indexed: 01/11/2024] Open
Abstract
Plant and pollinator communities are vital for transnational food chains. Like many natural systems, they are affected by global change: rapidly deteriorating conditions threaten their numbers. Previous theoretical studies identified the potential for community-wide collapse above critical levels of environmental stressors-so-called bifurcation-induced tipping points. Fortunately, even as conditions deteriorate, individuals have some adaptive capacity, potentially increasing the boundary for a safe operating space where changes in ecological processes are reversible. Our study considers this adaptive capacity of pollinators to resource availability and identifies a new threat to disturbed pollinator communities. We model the adaptive foraging of pollinators in changing environments. Pollinator's adaptive foraging alters the dynamical responses of species, to the advantage of some-typically generalists-and the disadvantage of others, with systematic non-linear and non-monotonic effects on the abundance of particular species. We show that, in addition to the extent of environmental stress, the pace of change of environmental stress can also lead to the early collapse of both adaptive and nonadaptive pollinator communities. Specifically, perturbed communities exhibit rate-induced tipping points at stress levels within the safe boundary defined for constant stressors. With adaptive foraging, tipping is a more asynchronous collapse of species compared to nonadaptive pollinator communities, meaning that not all pollinator species reach a tipping event simultaneously. These results suggest that it is essential to consider the adaptive capacity of pollinator communities for monitoring and conservation. Both the extent and the rate of stress change relative to the ability of communities to recover are critical environmental boundaries.
Collapse
Affiliation(s)
- Sjoerd Terpstra
- Graduate School of Informatics, University of Amsterdam, Amsterdam, The Netherlands
- Institute for Marine and Atmospheric Research Utrecht, Utrecht University, Utrecht, The Netherlands
- Institute for Advanced Study, University of Amsterdam, Amsterdam, The Netherlands
| | - Flávia M. D. Marquitti
- Instituto de Física ‘Gleb Wataghin’ & Programa de Pós Graduação em Ecologia, Universidade Estadual de Campinas, Campinas, São Paulo, Brazil
- International Centre for Theoretical Physics - South American Institute for Fundamental Research (ICTP-SAIFR), São Paulo, São Paulo, Brazil
| | - Vítor V. Vasconcelos
- Institute for Advanced Study, University of Amsterdam, Amsterdam, The Netherlands
- Computational Science Lab, Informatics Institute, University of Amsterdam, Amsterdam, The Netherlands
| |
Collapse
|
15
|
Banerjee A, Pavithran I, Sujith RI. Early warnings of tipping in a non-autonomous turbulent reactive flow system: Efficacy, reliability, and warning times. CHAOS (WOODBURY, N.Y.) 2024; 34:013113. [PMID: 38198675 DOI: 10.1063/5.0160918] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Accepted: 12/04/2023] [Indexed: 01/12/2024]
Abstract
Real-world complex systems such as the earth's climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit aperiodic fluctuations, either chaotic or stochastic in nature. Often, the parameters describing a system vary with time, showing time dependency. Constrained by these effects, it becomes difficult to be warned of an impending critical transition, as such effects contaminate the precursory signals of the transition. Therefore, a need for efficient and reliable early-warning signals (EWSs) in such complex systems is in pressing demand. Motivated by this fact, in the present work, we analyze various EWSs in the context of a non-autonomous turbulent thermoacoustic system. In particular, we investigate the efficacy of different EWS in forecasting the onset of thermoacoustic instability (TAI) and their reliability with respect to the rate of change of the control parameter. This is the first experimental study of tipping points in a non-autonomous turbulent thermoacoustic system. We consider the Reynolds number (Re) as the control parameter, which is varied linearly with time at finite rates. The considered EWSs are derived from critical slowing down, spectral properties, and fractal characteristics of the system variables. The state of TAI is associated with large amplitude acoustic pressure oscillations that could lead thermoacoustic systems to break down. We consider acoustic pressure fluctuations as a potential system variable to perform the analysis. Our analysis shows that irrespective of the rate of variation of the control parameter, the Hurst exponent and variance of autocorrelation coefficients warn of an impending transition well in advance and are more reliable than other EWS measures. Additionally, we show the variation in the warning time to an impending TAI with rates of change of the control parameter. We also investigate the variation in amplitudes of the most significant modes of acoustic pressure oscillations with the Hurst exponent. Such variations lead to scaling laws that could be significant in prediction and devising control actions to mitigate TAI.
Collapse
Affiliation(s)
- Ankan Banerjee
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
- Center of Excellence for Studying Critical Transitions in Complex Systems, Indian Institute of Technology Madras, Chennai 600036, India
| | - Induja Pavithran
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
- Center of Excellence for Studying Critical Transitions in Complex Systems, Indian Institute of Technology Madras, Chennai 600036, India
| | - R I Sujith
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
- Center of Excellence for Studying Critical Transitions in Complex Systems, Indian Institute of Technology Madras, Chennai 600036, India
| |
Collapse
|
16
|
Panahi S, Do Y, Hastings A, Lai YC. Rate-induced tipping in complex high-dimensional ecological networks. Proc Natl Acad Sci U S A 2023; 120:e2308820120. [PMID: 38091288 PMCID: PMC10743502 DOI: 10.1073/pnas.2308820120] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 11/15/2023] [Indexed: 12/24/2023] Open
Abstract
In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we find a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: Only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.
Collapse
Affiliation(s)
- Shirin Panahi
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ85287
| | - Younghae Do
- Department of Mathematics, Nonlinear Dynamics Mathematical Application Center, Kyungpook National University, Daegu41566, Republic of Korea
| | - Alan Hastings
- Department of Environmental Science and Policy, University of California, Davis, CA95616
- Santa Fe Institute, Santa Fe, NM87501
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ85287
- Department of Physics, Arizona State University, Tempe, AZ85287
| |
Collapse
|
17
|
Heino MTJ, Proverbio D, Marchand G, Resnicow K, Hankonen N. Attractor landscapes: a unifying conceptual model for understanding behaviour change across scales of observation. Health Psychol Rev 2023; 17:655-672. [PMID: 36420691 PMCID: PMC10261543 DOI: 10.1080/17437199.2022.2146598] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Accepted: 11/07/2022] [Indexed: 11/25/2022]
Abstract
Models and theories in behaviour change science are not in short supply, but they almost exclusively pertain to a particular facet of behaviour, such as automaticity or reasoned action, or to a single scale of observation such as individuals or communities. We present a highly generalisable conceptual model which is widely used in complex systems research from biology to physics, in an accessible form to behavioural scientists. The proposed model of attractor landscapes can be used to understand human behaviour change on different levels, from individuals to dyads, groups and societies. We use the model as a tool to present neglected ideas in contemporary behaviour change science, such as hysteresis and nonlinearity. The model of attractor landscapes can deepen understanding of well-known features of behaviour change (research), including short-livedness of intervention effects, problematicity of focusing on behavioural initiation while neglecting behavioural maintenance, continuum and stage models of behaviour change understood within a single accommodating framework, and the concept of resilience. We also demonstrate potential methods of analysis and outline avenues for future research.
Collapse
Affiliation(s)
| | | | | | - Kenneth Resnicow
- School of Public Health, University of Michigan. Rogel Cancer Center University of Michigan
| | | |
Collapse
|
18
|
Ehstand N, Donner RV, López C, Hernández-García E. Network percolation provides early warnings of abrupt changes in coupled oscillatory systems: An explanatory analysis. Phys Rev E 2023; 108:054207. [PMID: 38115534 DOI: 10.1103/physreve.108.054207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 10/02/2023] [Indexed: 12/21/2023]
Abstract
Functional networks are powerful tools to study statistical interdependency structures in spatially extended or multivariable systems. They have been used to get insights into the dynamics of complex systems in various areas of science. In particular, percolation properties of correlation networks have been employed to identify early warning signals of critical transitions. In this work, we further investigate the corresponding potential of percolation measures for the anticipation of different types of sudden shifts in the state of coupled irregularly oscillating systems. As a paradigmatic model system, we study the dynamics of a ring of diffusively coupled noisy FitzHugh-Nagumo oscillators and show that, when the oscillators are nearly completely synchronized, the percolation-based precursors successfully provide very early warnings of the rapid switches between the two states of the system. We clarify the mechanisms behind the percolation transition by separating global trends given by the mean-field behavior from the synchronization of individual stochastic fluctuations. We then apply the same methodology to real-world data of sea surface temperature anomalies during different phases of the El Niño-Southern Oscillation. This leads to a better understanding of the factors that make percolation precursors effective as early warning indicators of incipient El Niño and La Niña events.
Collapse
Affiliation(s)
- Noémie Ehstand
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Reik V Donner
- Department of Water, Environment, Construction and Safety, Magdeburg-Stendal University of Applied Sciences, Breitscheidstraße 2, D-39114 Magdeburg, Germany
- Research Department IV-Complexity Science and Research Department I-Earth System Analysis, Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Telegrafenberg A31, D-14473 Potsdam, Germany
| | - Cristóbal López
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Emilio Hernández-García
- IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| |
Collapse
|
19
|
Chekroun MD, Liu H, McWilliams JC. Optimal parameterizing manifolds for anticipating tipping points and higher-order critical transitions. CHAOS (WOODBURY, N.Y.) 2023; 33:093126. [PMID: 37729098 DOI: 10.1063/5.0167419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2023] [Accepted: 08/31/2023] [Indexed: 09/22/2023]
Abstract
A general, variational approach to derive low-order reduced models from possibly non-autonomous systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes more classical notions of invariant or slow manifolds when the breakdown of "slaving" occurs, i.e., when the unresolved variables cannot be expressed as an exact functional of the resolved ones anymore. The OPM provides, within a given class of parameterizations of the unresolved variables, the manifold that averages out optimally these variables as conditioned on the resolved ones. The class of parameterizations retained here is that of continuous deformations of parameterizations rigorously valid near the onset of instability. These deformations are produced through the integration of auxiliary backward-forward systems built from the model's equations and lead to analytic formulas for parameterizations. In this modus operandi, the backward integration time is the key parameter to select per scale/variable to parameterize in order to derive the relevant parameterizations which are doomed to be no longer exact away from instability onset due to the breakdown of slaving typically encountered, e.g., for chaotic regimes. The selection criterion is then made through data-informed minimization of a least-square parameterization defect. It is thus shown through optimization of the backward integration time per scale/variable to parameterize, that skilled OPM reduced systems can be derived for predicting with accuracy higher-order critical transitions or catastrophic tipping phenomena, while training our parameterization formulas for regimes prior to these transitions takes place.
Collapse
Affiliation(s)
- Mickaël D Chekroun
- Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095-1565, USA and Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel
| | - Honghu Liu
- Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061, USA
| | - James C McWilliams
- Department of Atmospheric and Oceanic Sciences and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90095-1565, USA
| |
Collapse
|
20
|
Cantisán J, Yanchuk S, Seoane JM, Sanjuán MAF, Kurths J. Rate and memory effects in bifurcation-induced tipping. Phys Rev E 2023; 108:024203. [PMID: 37723724 DOI: 10.1103/physreve.108.024203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2023] [Accepted: 07/20/2023] [Indexed: 09/20/2023]
Abstract
A variation in the environment of a system, such as the temperature, the concentration of a chemical solution, or the appearance of a magnetic field, may lead to a drift in one of the parameters. If the parameter crosses a bifurcation point, the system can tip from one attractor to another (bifurcation-induced tipping). Typically, this stability exchange occurs at a parameter value beyond the bifurcation value. This is what we call, here, the shifted stability exchange. We perform a systematic study on how the shift is affected by the initial parameter value and its change rate. To that end, we present numerical simulations and partly analytical results for different types of bifurcations and different paradigmatic systems. We show that the nonautonomous dynamics can be split into two regimes. Depending on whether we exceed the numerical or experimental precision or not, the system may enter the nondeterministic or the deterministic regime. This is determined solely by the conditions of the drift. Finally, we deduce the scaling laws governing this phenomenon and we observe very similar behavior for different systems and different bifurcations in both regimes.
Collapse
Affiliation(s)
- Julia Cantisán
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Serhiy Yanchuk
- Department of Mathematics, Humboldt University Berlin, 12489 Berlin, Germany
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
| | - Jesús M Seoane
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos Tulipán s/n, 28933 Móstoles, Madrid, Spain
| | - Miguel A F Sanjuán
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos Tulipán s/n, 28933 Móstoles, Madrid, Spain
- Department of Applied Informatics, Kaunas University of Technology Studentu 50-415, Kaunas LT-51368, Lithuania
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany
- Department of Physics, Humboldt University Berlin, 12489 Berlin, Germany
| |
Collapse
|
21
|
Ditlevsen P, Ditlevsen S. Warning of a forthcoming collapse of the Atlantic meridional overturning circulation. Nat Commun 2023; 14:4254. [PMID: 37491344 PMCID: PMC10368695 DOI: 10.1038/s41467-023-39810-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2023] [Accepted: 06/29/2023] [Indexed: 07/27/2023] Open
Abstract
The Atlantic meridional overturning circulation (AMOC) is a major tipping element in the climate system and a future collapse would have severe impacts on the climate in the North Atlantic region. In recent years weakening in circulation has been reported, but assessments by the Intergovernmental Panel on Climate Change (IPCC), based on the Climate Model Intercomparison Project (CMIP) model simulations suggest that a full collapse is unlikely within the 21st century. Tipping to an undesired state in the climate is, however, a growing concern with increasing greenhouse gas concentrations. Predictions based on observations rely on detecting early-warning signals, primarily an increase in variance (loss of resilience) and increased autocorrelation (critical slowing down), which have recently been reported for the AMOC. Here we provide statistical significance and data-driven estimators for the time of tipping. We estimate a collapse of the AMOC to occur around mid-century under the current scenario of future emissions.
Collapse
Affiliation(s)
- Peter Ditlevsen
- Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
| | - Susanne Ditlevsen
- Institute of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark.
| |
Collapse
|
22
|
Proverbio D, Skupin A, Gonçalves J. Systematic analysis and optimization of early warning signals for critical transitions using distribution data. iScience 2023; 26:107156. [PMID: 37456849 PMCID: PMC10338236 DOI: 10.1016/j.isci.2023.107156] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Revised: 04/21/2023] [Accepted: 06/12/2023] [Indexed: 07/18/2023] Open
Abstract
Abrupt shifts between alternative regimes occur in complex systems, from cell regulation to brain functions to ecosystems. Several model-free early warning signals (EWS) have been proposed to detect impending transitions, but failure or poor performance in some systems have called for better investigation of their generic applicability. Notably, there are still ongoing debates whether such signals can be successfully extracted from data in particular from biological experiments. In this work, we systematically investigate properties and performance of dynamical EWS in different deteriorating conditions, and we propose an optimized combination to trigger warnings as early as possible, eventually verified on experimental data from microbiological populations. Our results explain discrepancies observed in the literature between warning signs extracted from simulated models and from real data, provide guidance for EWS selection based on desired systems and suggest an optimized composite indicator to alert for impending critical transitions using distribution data.
Collapse
Affiliation(s)
- Daniele Proverbio
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- National Center for Microscopy and Imaging Research, University of California San Diego, Gilman Drive, La Jolla, CA 9500, USA
- Department of Physics and Material Science, University of Luxembourg, 162a Avenue de La Faiencerie, 1511 Luxembourg, Luxembourg
| | - Jorge Gonçalves
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue Du Swing, 4367 Belvaux, Luxembourg
- Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK
| |
Collapse
|
23
|
Datseris G, Luiz Rossi K, Wagemakers A. Framework for global stability analysis of dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:073151. [PMID: 37499248 DOI: 10.1063/5.0159675] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 07/03/2023] [Indexed: 07/29/2023]
Abstract
Dynamical systems that are used to model power grids, the brain, and other physical systems can exhibit coexisting stable states known as attractors. A powerful tool to understand such systems, as well as to better predict when they may "tip" from one stable state to the other, is global stability analysis. It involves identifying the initial conditions that converge to each attractor, known as the basins of attraction, measuring the relative volume of these basins in state space, and quantifying how these fractions change as a system parameter evolves. By improving existing approaches, we present a comprehensive framework that allows for global stability analysis of dynamical systems. Notably, our framework enables the analysis to be made efficiently and conveniently over a parameter range. As such, it becomes an essential tool for stability analysis of dynamical systems that goes beyond local stability analysis offered by alternative frameworks. We demonstrate the effectiveness of our approach on a variety of models, including climate, power grids, ecosystems, and more. Our framework is available as simple-to-use open-source code as part of the DynamicalSystems.jl library.
Collapse
Affiliation(s)
- George Datseris
- Department of Mathematics and Statistics, University of Exeter, North Park Road, Exeter EX4 4QF, United Kingdom
| | - Kalel Luiz Rossi
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, Carl-von-Ossietzky-Straße 9-11, 26111 Oldenburg, Germany
| | - Alexandre Wagemakers
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, 28933 Móstoles, Madrid, Spain
| |
Collapse
|
24
|
Brunetti M, Ragon C. Attractors and bifurcation diagrams in complex climate models. Phys Rev E 2023; 107:054214. [PMID: 37329063 DOI: 10.1103/physreve.107.054214] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 03/28/2023] [Indexed: 06/18/2023]
Abstract
The climate is a complex nonequilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the possible steady states under different forcing is the bifurcation diagram, which reveals the regions of multistability, the position of tipping points, and the range of stability of each steady state. However, its construction is highly time consuming in climate models with a dynamical deep ocean, whose relaxation time is of the order of thousand years, or other feedback mechanisms that act on even longer time scales, like continental ice or carbon cycle. Using a coupled setup of the MIT general circulation model, we test two techniques for the construction of bifurcation diagrams with complementary advantages and reduced execution time. The first is based on the introduction of random fluctuations in the forcing and permits to explore a wide part of phase space. The second reconstructs the stable branches using estimates of the internal variability and of the surface energy imbalance on each attractor, and is more precise in finding the position of tipping points.
Collapse
Affiliation(s)
- Maura Brunetti
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Bd. Carl-Vogt 66, CH-1205 Geneva, Switzerland
| | - Charline Ragon
- Group of Applied Physics and Institute for Environmental Sciences, University of Geneva, Bd. Carl-Vogt 66, CH-1205 Geneva, Switzerland
| |
Collapse
|
25
|
Setty S, Cramwinckel MJ, van Nes EH, van de Leemput IA, Dijkstra HA, Lourens LJ, Scheffer M, Sluijs A. Loss of Earth system resilience during early Eocene transient global warming events. SCIENCE ADVANCES 2023; 9:eade5466. [PMID: 37027462 PMCID: PMC10081840 DOI: 10.1126/sciadv.ade5466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/23/2022] [Accepted: 03/06/2023] [Indexed: 06/19/2023]
Abstract
Superimposed on long-term late Paleocene-early Eocene warming (~59 to 52 million years ago), Earth's climate experienced a series of abrupt perturbations, characterized by massive carbon input into the ocean-atmosphere system and global warming. Here, we examine the three most punctuated events of this period, the Paleocene-Eocene Thermal Maximum and Eocene Thermal Maximum 2 and 3, to probe whether they were initiated by climate-driven carbon cycle tipping points. Specifically, we analyze the dynamics of climate and carbon cycle indicators acquired from marine sediments to detect changes in Earth system resilience and to identify positive feedbacks. Our analyses suggest a loss of Earth system resilience toward all three events. Moreover, dynamic convergent cross mapping reveals intensifying coupling between the carbon cycle and climate during the long-term warming trend, supporting increasingly dominant climate forcing of carbon cycle dynamics during the Early Eocene Climatic Optimum when these recurrent global warming events became more frequent.
Collapse
Affiliation(s)
- Shruti Setty
- Department of Environmental Science, Wageningen University and Research, Droevendaalsesteeg 3a, 6708 PB Wageningen, Netherlands
| | - Margot J. Cramwinckel
- Department of Earth Sciences, Faculty of Geoscience, Utrecht University, Princetonlaan 8a, 3584 CB Utrecht, Netherlands
| | - Egbert H. van Nes
- Department of Environmental Science, Wageningen University and Research, Droevendaalsesteeg 3a, 6708 PB Wageningen, Netherlands
| | - Ingrid A. van de Leemput
- Department of Environmental Science, Wageningen University and Research, Droevendaalsesteeg 3a, 6708 PB Wageningen, Netherlands
| | - Henk A. Dijkstra
- Institute for Marine and Atmospheric research Utrecht, Department of Physics, Utrecht University, Princetonlaan 5, 3584 CC Utrecht, Netherlands
- Centre for Complex Systems Studies, Utrecht University, Princetonlaan 5, 3584 CC Utrecht, Netherlands
| | - Lucas J Lourens
- Department of Earth Sciences, Faculty of Geoscience, Utrecht University, Princetonlaan 8a, 3584 CB Utrecht, Netherlands
| | - Marten Scheffer
- Department of Environmental Science, Wageningen University and Research, Droevendaalsesteeg 3a, 6708 PB Wageningen, Netherlands
| | - Appy Sluijs
- Department of Earth Sciences, Faculty of Geoscience, Utrecht University, Princetonlaan 8a, 3584 CB Utrecht, Netherlands
| |
Collapse
|
26
|
Eckert N, Rusch G, Lyytimäki J, Lepenies R, Giacona F, Panzacchi M, Mosoni C, Pedersen AB, Mustajoki J, Mille R, Richard D, Jax K. Sustainable Development Goals and risks: The Yin and the Yang of the paths towards sustainability. AMBIO 2023; 52:683-701. [PMID: 36369605 PMCID: PMC9989090 DOI: 10.1007/s13280-022-01800-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2022] [Revised: 09/30/2022] [Accepted: 10/03/2022] [Indexed: 06/16/2023]
Abstract
The United Nations 2030 Agenda and Sustainable Development Goals (SDGs) define a path towards a sustainable future, but given that uncertainty characterises the outcomes of any SDG-related actions, risks in the implementation of the Agenda need to be addressed. At the same time, most risk assessments are narrowed to sectoral approaches and do not refer to SDGs. Here, on the basis of a literature review and workshops, it is analysed how SDGs and risks relate to each other's in different communities. Then, it is formally demonstrated that, as soon as the mathematical definition of risks is broadened to embrace a more systemic perspective, acting to maintain socio-environmental systems within their sustainability domain can be done by risk minimisation. This makes Sustainable Development Goals and risks "the Yin and the Yang of the paths towards sustainability". Eventually, the usefulness of the SDG-risk nexus for both sustainability and risk management is emphasized.
Collapse
Affiliation(s)
- Nicolas Eckert
- INRAE, UR ETNA / Université Grenoble Alpes, 2 rue de la papeterie, 38402 St Martin d’Heres, France
| | - Graciela Rusch
- Norwegian Institute for Nature Research, Torgarden, P.O. Box 5685, 7485 Trondheim, Norway
| | - Jari Lyytimäki
- Finnish Environment Institute (SYKE), Latokartanonkaari 11, 00790 Helsinki, Finland
| | - Robert Lepenies
- Karlshochschule International University, Karlstrasse 26-28, 71633 Karlsruhe, Germany
| | - Florie Giacona
- INRAE, UR ETNA / Université Grenoble Alpes, 2 rue de la papeterie, 38402 St Martin d’Heres, France
| | - Manuela Panzacchi
- Norwegian Institute for Nature Research, Torgarden, P.O. Box 5685, 7485 Trondheim, Norway
| | - Claire Mosoni
- Finnish Environment Institute (SYKE), Latokartanonkaari 11, 00790 Helsinki, Finland
| | - Anders Branth Pedersen
- Department of Environmental Science, Aarhus University, Frederiksborgvej 399, 4000 Roskilde, Denmark
| | - Jyri Mustajoki
- Finnish Environment Institute (SYKE), Latokartanonkaari 11, 00790 Helsinki, Finland
| | - Raoul Mille
- French Permanent Mission, 52 Corso del Rinascimento, 00186 Rome, Italy
| | - Didier Richard
- INRAE, 2 rue de la papeterie, BP76, 38402 Saint-Martin-d’Hères Cedex, France
| | - Kurt Jax
- Department of Conservation Biology and Social-Ecological Systems, Helmholtz-Centre for Environmental Research – UFZ, Permoserstr. 15, 04318 Leipzig, Germany
| |
Collapse
|
27
|
Rakhshan SA, Nejad MS, Zaj M, Ghane FH. Global analysis and prediction scenario of infectious outbreaks by recurrent dynamic model and machine learning models: A case study on COVID-19. Comput Biol Med 2023; 158:106817. [PMID: 36989749 PMCID: PMC10035804 DOI: 10.1016/j.compbiomed.2023.106817] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2022] [Revised: 03/10/2023] [Accepted: 03/20/2023] [Indexed: 03/25/2023]
Abstract
It is essential to evaluate patient outcomes at an early stage when dealing with a pandemic to provide optimal clinical care and resource management. Many methods have been proposed to provide a roadmap against different pandemics, including the recent pandemic disease COVID-19. Due to recurrent epidemic waves of COVID-19, which have been observed in many countries, mathematical modeling and forecasting of COVID-19 are still necessary as long as the world continues to battle against the pandemic. Modeling may aid in determining which interventions to try or predict future growth patterns. In this article, we design a combined approach for analyzing any pandemic in two separate parts. In the first part of the paper, we develop a recurrent SEIRS compartmental model to predict recurrent outbreak patterns of diseases. Due to its time-varying parameters, our model is able to reflect the dynamics of infectious diseases, and to measure the effectiveness of the restrictive measures. We discuss the stable solutions of the corresponding autonomous system with frozen parameters. We focus on the regime shifts and tipping points; then we investigate tipping phenomena due to parameter drifts in our time-varying parameters model that exhibits a bifurcation in the frozen-in case. Furthermore, we propose an optimal numerical design for estimating the system’s parameters. In the second part, we introduce machine learning models to strengthen the methodology of our paper in data analysis, particularly for prediction scenarios. We use MLP, RBF, LSTM, ANFIS, and GRNN for training and evaluation of COVID-19. Then, we compare the results with the recurrent dynamical system in the fitting process and prediction scenario. We also confirm results by implementing our methods on the released data on COVID-19 by WHO for Italy, Germany, Iran, and South Africa between 1/22/2020 and 7/24/2021, when people were engaged with different variants including Alpha, Beta, Gamma, and Delta. The results of this article show that the dynamic model is adequate for long-term analysis and data fitting, as well as obtaining parameters affecting the epidemic. However, it is ineffective in providing a long-term forecast. In contrast machine learning methods effectively provide disease prediction, although they do not provide analysis such as dynamic models. Finally, some metrics, including RMSE, R-Squared, and accuracy, are used to evaluate the machine learning models. These metrics confirm that ANFIS and RBF perform better than other methods in training and testing zones.
Collapse
Affiliation(s)
| | - Mahdi Soltani Nejad
- Department of Railway Engineering, Iran University of Science and Technology, Iran
| | - Marzie Zaj
- Department of Mathematics, Ferdowsi University of Mashhad, Iran
| | | |
Collapse
|
28
|
Time-scale synchronisation of oscillatory responses can lead to non-monotonous R-tipping. Sci Rep 2023; 13:2104. [PMID: 36747023 PMCID: PMC9902488 DOI: 10.1038/s41598-023-28771-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2022] [Accepted: 01/24/2023] [Indexed: 02/08/2023] Open
Abstract
Rate-induced tipping (R-tipping) describes the fact that, for multistable dynamic systems, an abrupt transition can take place not only because of the forcing magnitude, but also because of the forcing rate. In the present work, we demonstrate through the case study of a piecewise-linear oscillator (PLO), that increasing the rate of forcing can make the system tip in some cases but might also prevent it from tipping in others. This counterintuitive effect is further called non-monotonous R-tipping (NMRT) and has already been observed in recent studies. We show that, in the present case, the reason for NMRT is the peak synchronisation of oscillatory responses operating on different time scales. We further illustrate that NMRT can be observed even in the presence of additive white noise of intermediate amplitude. Finally, NMRT is also observed on a van-der-Pol oscillator with an unstable limit cycle, suggesting that this effect is not limited to systems with a discontinuous right-hand side such as the PLO. This insight might be highly valuable, as the current research on tipping elements is shifting from an equilibrium to a dynamic perspective while using models of increasing complexity, in which NMRT might be observed but hard to understand.
Collapse
|
29
|
Sunny EM, Balakrishnan J, Kurths J. Predicting climatic tipping points. CHAOS (WOODBURY, N.Y.) 2023; 33:021101. [PMID: 36859203 DOI: 10.1063/5.0135266] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2022] [Accepted: 01/09/2023] [Indexed: 06/18/2023]
Abstract
Increased levels of greenhouse gases in the atmosphere, especially carbon dioxide, are leading contributors to a significant increase in the global temperature, and the consequent global climatic changes are more noticeable in recent years than in the past. A persistent increased growth of such gases might lead to an irreversible transition or tipping of the Earth's climatic system to a new dynamical state. A change of regimes in CO 2 buildup being correlated to one in global climate patterns, predicting this tipping point becomes crucially important. We propose here an innovative conceptual model, which does just this. Using the idea of rate-induced bifurcations, we show that a sufficiently rapid change in the system parameters beyond a critical value tips the system over to a new dynamical state. Our model when applied to real-world data detects tipping points, enables calculation of tipping rates and predicts their future values, and identifies thresholds beyond which tipping occurs. The model well captures the growth in time of the total global atmospheric fossil-fuel CO 2 concentrations, identifying regime shift changes through measurable parameters and enabling prediction of future trends based on past data. Our model shows two distinct routes to tipping. We predict that with the present trend of variation of atmospheric greenhouse gas concentrations, the Earth's climatic system would move over to a new stable dynamical regime in the year 2022. We determine a limit of 10.62 GtC at the start of 2022 for global CO 2 emissions in order to avoid this tipping.
Collapse
Affiliation(s)
- Eros M Sunny
- School of Natural Sciences and Engineering, National Institute of Advanced Studies (NIAS), Indian Institute of Science Campus, Bangalore 560012, India
| | - Janaki Balakrishnan
- School of Natural Sciences and Engineering, National Institute of Advanced Studies (NIAS), Indian Institute of Science Campus, Bangalore 560012, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, PO Box 601203, Potsdam 14412, Germany
| |
Collapse
|
30
|
Bastiaansen R, Ashwin P, von der Heydt AS. Climate response and sensitivity: time scales and late tipping points. Proc Math Phys Eng Sci 2023. [DOI: 10.1098/rspa.2022.0483] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Climate response metrics are used to quantify the Earth’s climate response to anthropogenic changes of atmospheric
CO
2
. Equilibrium climate sensitivity (ECS) is one such metric that measures the equilibrium response to
CO
2
doubling. However, both in their estimation and their usage, such metrics make assumptions on the linearity of climate response, although it is known that, especially for larger forcing levels, response can be nonlinear. Such nonlinear responses may become visible immediately in response to a larger perturbation, or may only become apparent after a long transient period. In this paper, we illustrate some potential problems and caveats when estimating ECS from transient simulations. We highlight ways that very slow time scales may lead to poor estimation of ECS even if there is seemingly good fit to linear response over moderate time scales. Moreover, such slow processes might lead to late abrupt responses (late tipping points) associated with a system’s nonlinearities. We illustrate these ideas using simulations on a global energy balance model with dynamic albedo. We also discuss the implications for estimating ECS for global climate models, highlighting that it is likely to remain difficult to make definitive statements about the simulation times needed to reach an equilibrium.
Collapse
Affiliation(s)
- Robbin Bastiaansen
- Department of Physics and IMAU, Utrecht University, Utrecht, The Netherlands
- Mathematical Institute, Utrecht University, Utrecht, The Netherlands
| | - Peter Ashwin
- Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, UK
| | | |
Collapse
|
31
|
Pershin A, Beaume C, Li K, Tobias SM. Training a neural network to predict dynamics it has never seen. Phys Rev E 2023; 107:014304. [PMID: 36797895 DOI: 10.1103/physreve.107.014304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2022] [Accepted: 12/15/2022] [Indexed: 01/24/2023]
Abstract
Neural networks have proven to be remarkably successful for a wide range of complicated tasks, from image recognition and object detection to speech recognition and machine translation. One of their successes lies in their ability to predict future dynamics given a suitable training data set. Previous studies have shown how echo state networks (ESNs), a type of recurrent neural networks, can successfully predict both short-term and long-term dynamics of even chaotic systems. This study shows that, remarkably, ESNs can successfully predict dynamical behavior that is qualitatively different from any behavior contained in their training set. Evidence is provided for a fluid dynamics problem where the flow can transition between laminar (ordered) and turbulent (seemingly disordered) regimes. Despite being trained on the turbulent regime only, ESNs are found to predict the existence of laminar behavior. Moreover, the statistics of turbulent-to-laminar and laminar-to-turbulent transitions are also predicted successfully. The utility of ESNs in acting as early-warning generators for transition is discussed. These results are expected to be widely applicable to data-driven modeling of temporal behavior in a range of physical, climate, biological, ecological, and finance models characterized by the presence of tipping points and sudden transitions between several competing states.
Collapse
Affiliation(s)
- Anton Pershin
- Atmospheric, Oceanic and Planetary Physics, University of Oxford, Oxford, United Kingdom and School of Mathematics, University of Leeds, Leeds, OX1 3PU United Kingdom
| | - Cédric Beaume
- School of Mathematics, University of Leeds, Leeds, LS2 9JT United Kingdom
| | - Kuan Li
- School of Mathematics, University of Leeds, Leeds, LS2 9JT United Kingdom
| | - Steven M Tobias
- School of Mathematics, University of Leeds, Leeds, LS2 9JT United Kingdom
| |
Collapse
|
32
|
Slyman K, Jones CK. Rate and noise-induced tipping working in concert. CHAOS (WOODBURY, N.Y.) 2023; 33:013119. [PMID: 36725643 DOI: 10.1063/5.0129341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2022] [Accepted: 12/19/2022] [Indexed: 06/18/2023]
Abstract
Rate-induced tipping occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states. We show that the addition of noise to the system can cause it to tip well below the critical rate at which rate-induced tipping would occur. Moreover, it does so with significantly increased probability over the noise acting alone. We achieve this by finding a global minimizer in a canonical problem of the Freidlin-Wentzell action functional of large deviation theory that represents the most probable path for tipping. This is realized as a heteroclinic connection for the Euler-Lagrange system associated with the Freidlin-Wentzell action and we find it exists for all rates less than or equal to the critical rate. Its role as the most probable path is corroborated by direct Monte Carlo simulations.
Collapse
Affiliation(s)
- Katherine Slyman
- Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27517, USA
| | - Christopher K Jones
- Renaissance Computing Institute, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27517, USA
| |
Collapse
|
33
|
Synodinos AD, Karnatak R, Aguilar‐Trigueros CA, Gras P, Heger T, Ionescu D, Maaß S, Musseau CL, Onandia G, Planillo A, Weiss L, Wollrab S, Ryo M. The rate of environmental change as an important driver across scales in ecology. OIKOS 2022. [DOI: 10.1111/oik.09616] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Alexis D. Synodinos
- Theoretical and Experimental Ecology Station, CNRS Moulis France
- Plant Ecology and Nature Conservation, Univ. of Potsdam Potsdam Germany
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
| | - Rajat Karnatak
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Leibniz Inst. of Freshwater Ecology and Inland Fisheries Berlin Germany
| | - Carlos A. Aguilar‐Trigueros
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Freie Universität Berlin, Inst. of Biology Berlin Germany
| | - Pierre Gras
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Dept of Ecological Dynamics, Leibniz Inst. for Zoo and Wildlife Research (IZW) Berlin Germany
| | - Tina Heger
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Leibniz Inst. of Freshwater Ecology and Inland Fisheries Berlin Germany
- Freie Universität Berlin, Inst. of Biology Berlin Germany
- Biodiversity Research/Botany, Univ. of Potsdam Potsdam Germany
- Restoration Ecology, Technical Univ. of Munich Freising Germany
| | - Danny Ionescu
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Leibniz Inst. of Freshwater Ecology and Inland Fisheries (IGB) Neuglobsow Germany
| | - Stefanie Maaß
- Plant Ecology and Nature Conservation, Univ. of Potsdam Potsdam Germany
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
| | - Camille L. Musseau
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Dept of Biology, Chemistry, Pharmacy, Inst. of Biology, Freie Univ. Berlin Berlin Germany
- Leibniz Inst.I of Freshwater Ecology and Inland Fisheries (IGB) Berlin Germany
| | - Gabriela Onandia
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Research Platform Data Analysis and Simulation, Leibniz Centre for Agricultural Landscape Research (ZALF) Muencheberg Germany
| | - Aimara Planillo
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Dept of Ecological Dynamics, Leibniz Inst. for Zoo and Wildlife Research (IZW) Berlin Germany
| | - Lina Weiss
- Plant Ecology and Nature Conservation, Univ. of Potsdam Potsdam Germany
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
| | - Sabine Wollrab
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Leibniz Inst. of Freshwater Ecology and Inland Fisheries Berlin Germany
| | - Masahiro Ryo
- Berlin‐Brandenburg Inst. of Advanced Biodiversity Research Berlin Germany
- Research Platform Data Analysis and Simulation, Leibniz Centre for Agricultural Landscape Research (ZALF) Muencheberg Germany
- Environment and Natural Sciences, Brandenburg Univ. of Technology Cottbus‐Senftenberg Cottbus Germany
| |
Collapse
|
34
|
Heßler M, Kamps O. Quantifying resilience and the risk of regime shifts under strong correlated noise. PNAS NEXUS 2022; 2:pgac296. [PMID: 36743473 PMCID: PMC9896148 DOI: 10.1093/pnasnexus/pgac296] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/19/2022] [Accepted: 12/20/2022] [Indexed: 12/25/2022]
Abstract
Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.
Collapse
Affiliation(s)
| | - Oliver Kamps
- Center for Nonlinear Science, Westphalian Wilhelms-University Münster, Corrensstraße 2 48149, North Rhine-Westphalia, Germany
| |
Collapse
|
35
|
Rodal M, Krumscheid S, Madan G, Henry LaCasce J, Vercauteren N. Dynamical stability indicator based on autoregressive moving-average models: Critical transitions and the Atlantic meridional overturning circulation. CHAOS (WOODBURY, N.Y.) 2022; 32:113139. [PMID: 36456350 DOI: 10.1063/5.0089694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Accepted: 11/01/2022] [Indexed: 06/17/2023]
Abstract
A statistical indicator for dynamic stability, known as the Υ indicator, is used to gauge the stability and, hence, detect approaching tipping points of simulation data from a reduced five-box model of the North Atlantic Meridional Overturning Circulation (AMOC) exposed to a time-dependent hosing function. The hosing function simulates the influx of fresh water due to the melting of the Greenland ice sheet and increased precipitation in the North Atlantic. The Υ indicator is designed to detect changes in the memory properties of the dynamics and is based on fitting auto-regressive moving-average models in a sliding window approach to time series data. An increase in memory properties is interpreted as a sign of dynamical instability. The performance of the indicator is tested on time series subject to different types of tipping, namely, bifurcation-induced, noise-induced, and rate-induced tipping. The numerical analysis shows that the indicator indeed responds to the different types of induced instabilities. Finally, the indicator is applied to two AMOC time series from a full complexity Earth systems model (CESM2). Compared with the doubling CO scenario, the quadrupling CO scenario results in stronger dynamical instability of the AMOC during its weakening phase.
Collapse
Affiliation(s)
- Marie Rodal
- FB Mathematik und Informatik, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | | | - Gaurav Madan
- Section for Meteorology and Oceanography, Department of Geosciences, University of Oslo, Blindernveien 31, Kristine Bonnevies hus, 0371 Oslo, Norway
| | - Joseph Henry LaCasce
- Section for Meteorology and Oceanography, Department of Geosciences, University of Oslo, Blindernveien 31, Kristine Bonnevies hus, 0371 Oslo, Norway
| | - Nikki Vercauteren
- Section for Meteorology and Oceanography, Department of Geosciences, University of Oslo, Blindernveien 31, Kristine Bonnevies hus, 0371 Oslo, Norway
| |
Collapse
|
36
|
Kim T, Kadji H, Whalen AJ, Ashourvan A, Freeman E, Fried SI, Tadigadapa S, Schiff SJ. Thermal effects on neurons during stimulation of the brain. J Neural Eng 2022; 19:056029. [PMID: 36126646 PMCID: PMC9855718 DOI: 10.1088/1741-2552/ac9339] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Revised: 09/13/2022] [Accepted: 09/20/2022] [Indexed: 01/25/2023]
Abstract
All electric and magnetic stimulation of the brain deposits thermal energy in the brain. This occurs through either Joule heating of the conductors carrying current through electrodes and magnetic coils, or through dissipation of energy in the conductive brain.Objective.Although electrical interaction with brain tissue is inseparable from thermal effects when electrodes are used, magnetic induction enables us to separate Joule heating from induction effects by contrasting AC and DC driving of magnetic coils using the same energy deposition within the conductors. Since mammalian cortical neurons have no known sensitivity to static magnetic fields, and if there is no evidence of effect on spike timing to oscillating magnetic fields, we can presume that the induced electrical currents within the brain are below the molecular shot noise where any interaction with tissue is purely thermal.Approach.In this study, we examined a range of frequencies produced from micromagnetic coils operating below the molecular shot noise threshold for electrical interaction with single neurons.Main results.We found that small temperature increases and decreases of 1∘C caused consistent transient suppression and excitation of neurons during temperature change. Numerical modeling of the biophysics demonstrated that the Na-K pump, and to a lesser extent the Nernst potential, could account for these transient effects. Such effects are dependent upon compartmental ion fluxes and the rate of temperature change.Significance.A new bifurcation is described in the model dynamics that accounts for the transient suppression and excitation; in addition, we note the remarkable similarity of this bifurcation's rate dependency with other thermal rate-dependent tipping points in planetary warming dynamics. These experimental and theoretical findings demonstrate that stimulation of the brain must take into account small thermal effects that are ubiquitously present in electrical and magnetic stimulation. More sophisticated models of electrical current interaction with neurons combined with thermal effects will lead to more accurate modulation of neuronal activity.
Collapse
Affiliation(s)
- TaeKen Kim
- Department of Physics, The Pennsylvania State University, University Park, PA, United States of America
| | - Herve Kadji
- Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA, United States of America
- Department of Radiation Oncology, Hackensack Meridian Health Mountainside Medical Center, Montclair, NJ, United States of America
| | - Andrew J Whalen
- Department of Mechanical Engineering, The Pennsylvania State University, University Park, PA, United States of America
- Department of Neurosurgery, Harvard Medical School, Massachusetts General Hospital, Boston, MA, United States of America
| | - Arian Ashourvan
- Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA, United States of America
| | - Eugene Freeman
- Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, United States of America
- Honeywell International Aerospace Advanced Technology, Plymouth, MN, United States of America
| | - Shelley I Fried
- Department of Neurosurgery, Harvard Medical School, Massachusetts General Hospital, Boston, MA, United States of America
- Boston VA Healthcare System, Boston 02130, United States of America
| | - Srinivas Tadigadapa
- Department of Electrical Engineering, The Pennsylvania State University, University Park, PA, United States of America
- Department of Electrical and Computer Engineering, Northeastern University, Boston, MA, United States of America
| | - Steven J Schiff
- Department of Physics, The Pennsylvania State University, University Park, PA, United States of America
- Center for Neural Engineering, Department of Engineering Science and Mechanics, The Pennsylvania State University, University Park, PA, United States of America
- Department of Neurosurgery, Penn State College of Medicine, Hershey, PA 17033, United States of America
- Department of Neurosurgery, Yale University, 333 Cedar Street, TMP 410, New Haven, CT 06510, United States of America
| |
Collapse
|
37
|
Proverbio D, Montanari AN, Skupin A, Gonçalves J. Buffering variability in cell regulation motifs close to criticality. Phys Rev E 2022; 106:L032402. [PMID: 36266798 DOI: 10.1103/physreve.106.l032402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2022] [Accepted: 08/25/2022] [Indexed: 06/16/2023]
Abstract
Bistable biological regulatory systems need to cope with stochastic noise to fine tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative interactions buffer system variability, hampering noise-induced regime shifts. Our analysis also shows that, in the considered cooperativity range, impending regime shifts can be generically detected by statistical early warning signals from distributional data. Our generic framework, based on minimal models, can be used to extract robustness and variability properties of more complex models and empirical data close to criticality.
Collapse
Affiliation(s)
- Daniele Proverbio
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, 4367, Belvaux, Luxembourg
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, EX4 4QL, Exeter, United Kingdom
| | - Arthur N Montanari
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, 4367, Belvaux, Luxembourg
| | - Alexander Skupin
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, 4367, Belvaux, Luxembourg
- Department of Physics and Material Science, University of Luxembourg, 162a Avenue de la Faiencerie, 1511 Luxembourg, Luxembourg
- Department of Neuroscience, University of California San Diego, 9500 Gilman Drive, La Jolla, California, United States
| | - Jorge Gonçalves
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, 4367, Belvaux, Luxembourg
- Department of Plant Sciences, University of Cambridge, CB2 3EA, Cambridge, United Kingdom
| |
Collapse
|
38
|
Meng Y, Lai YC, Grebogi C. The fundamental benefits of multiplexity in ecological networks. J R Soc Interface 2022; 19:20220438. [PMID: 36167085 PMCID: PMC9514891 DOI: 10.1098/rsif.2022.0438] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2022] [Accepted: 09/01/2022] [Indexed: 11/12/2022] Open
Abstract
A tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. Climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. We investigate the tipping-point dynamics in multi-layer ecological networks supported by mutualism. We unveil a natural mechanism by which the occurrence of tipping points can be delayed by multiplexity that broadly describes the diversity of the species abundances, the complexity of the interspecific relationships, and the topology of linkages in ecological networks. For a double-layer system of pollinators and plants, coupling between the network layers occurs when there is dispersal of pollinator species. Multiplexity emerges as the dispersing species establish their presence in the destination layer and have a simultaneous presence in both. We demonstrate that the new mutualistic links induced by the dispersing species with the residence species have fundamental benefits to the well-being of the ecosystem in delaying the tipping point and facilitating species recovery. Articulating and implementing control mechanisms to induce multiplexity can thus help sustain certain types of ecosystems that are in danger of extinction as the result of environmental changes.
Collapse
Affiliation(s)
- Yu Meng
- Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King’s College, University of Aberdeen, AB24 3UE, UK
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Straße 38, Dresden 01187, Germany
- Center for Systems Biology Dresden, Pfotenhauerstraße 108, Dresden 01307, Germany
| | - Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA
- Department of Physics, Arizona State University, Tempe, AZ 85287, USA
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King’s College, University of Aberdeen, AB24 3UE, UK
| |
Collapse
|
39
|
Lu Y, Li Y, Duan J. Extracting stochastic governing laws by non-local Kramers-Moyal formulae. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2022; 380:20210195. [PMID: 35719068 DOI: 10.1098/rsta.2021.0195] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/27/2021] [Accepted: 11/11/2021] [Indexed: 06/15/2023]
Abstract
With the rapid development of computational techniques and scientific tools, great progress of data-driven analysis has been made to extract governing laws of dynamical systems from data. Despite the wide occurrences of non-Gaussian fluctuations, the effective data-driven methods to identify stochastic differential equations with non-Gaussian Lévy noise are relatively few so far. In this work, we propose a data-driven approach to extract stochastic governing laws with both (Gaussian) Brownian motion and (non-Gaussian) Lévy motion, from short bursts of simulation data. Specifically, we use the normalizing flows technology to estimate the transition probability density function (solution of non-local Fokker-Planck equations) from data, and then substitute it into the recently proposed non-local Kramers-Moyal formulae to approximate Lévy jump measure, drift coefficient and diffusion coefficient. We demonstrate that this approach can learn the stochastic differential equation with Lévy motion. We present examples with one- and two-dimensional decoupled and coupled systems to illustrate our method. This approach will become an effective tool for discovering stochastic governing laws and understanding complex dynamical behaviours. This article is part of the theme issue 'Data-driven prediction in dynamical systems'.
Collapse
Affiliation(s)
- Yubin Lu
- School of Mathematics and Statistics and Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China
| | - Yang Li
- School of Automation, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
| | - Jinqiao Duan
- Departments of Applied Mathematics and Physics, Illinois Institute of Technology, Chicago, IL 60616, USA
| |
Collapse
|
40
|
Kaur T, Sharathi Dutta P. Critical rates of climate warming and abrupt collapse of ecosystems. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0086] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In the age of climate warming, comprehension of ecosystems’ future is one of the pressing challenges to humanity. While most studies on climate warming focus on the ‘magnitude of change’ of the Earth’s temperature, the ‘rate’ at which it is increasing cannot be ruled out. Rapid warming has already caused sudden ecosystem transitions at numerous biodiversity hot spots; a mechanistic understanding of such transitions is crucial. Here, we study a slow–fast consumer–resource ecosystem interacting in rapid warming scenarios. Employing geometric singular perturbation theory, we find that while a gradual change in mean temperature may accord population persistence, a critical warming rate can drive the resource’s sudden collapse, termed a warming-induced abrupt transition. This further triggers the bottom-up effect, resulting in the extinction of the consumer. The difference between the optimum temperature of the resource’s growth rate and the habitat temperature is crucial in deciding the critical rate of warming. Consequently, species inhabiting extreme temperature regions are more susceptible to warming-induced collapse than those within intermediate temperature ranges. We find that stochastic fluctuations in the system can advance warming-induced transitions, and the efficacy of generic early warning signals to anticipate sudden transitions is challenged.
Collapse
Affiliation(s)
- Taranjot Kaur
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140 001, India
| | - Partha Sharathi Dutta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140 001, India
| |
Collapse
|
41
|
Manoj K, Pawar SA, Kurths J, Sujith RI. Rijke tube: A nonlinear oscillator. CHAOS (WOODBURY, N.Y.) 2022; 32:072101. [PMID: 35907738 DOI: 10.1063/5.0091826] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 06/16/2022] [Indexed: 06/15/2023]
Abstract
Dynamical systems theory has emerged as an interdisciplinary area of research to characterize the complex dynamical transitions in real-world systems. Various nonlinear dynamical phenomena and bifurcations have been discovered over the decades using different reduced-order models of oscillators. Different measures and methodologies have been developed theoretically to detect, control, or suppress the nonlinear oscillations. However, obtaining such phenomena experimentally is often challenging, time-consuming, and risky mainly due to the limited control of certain parameters during experiments. With this review, we aim to introduce a paradigmatic and easily configurable Rijke tube oscillator to the dynamical systems community. The Rijke tube is commonly used by the combustion community as a prototype to investigate the detrimental phenomena of thermoacoustic instability. Recent investigations in such Rijke tubes have utilized various methodologies from dynamical systems theory to better understand the occurrence of thermoacoustic oscillations and their prediction and mitigation, both experimentally and theoretically. The existence of various dynamical behaviors has been reported in single and coupled Rijke tube oscillators. These behaviors include bifurcations, routes to chaos, noise-induced transitions, synchronization, and suppression of oscillations. Various early warning measures have been established to predict thermoacoustic instabilities. Therefore, this review article consolidates the usefulness of a Rijke tube oscillator in terms of experimentally discovering and modeling different nonlinear phenomena observed in physics, thus transcending the boundaries between the physics and the engineering communities.
Collapse
Affiliation(s)
- Krishna Manoj
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Samadhan A Pawar
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Potsdam 14473, Germany
| | - R I Sujith
- Department of Aerospace Engineering, Indian Institute of Technology Madras, Chennai 600036, India
| |
Collapse
|
42
|
Arnscheidt CW, Rothman DH. Rate-induced collapse in evolutionary systems. J R Soc Interface 2022; 19:20220182. [PMID: 35642430 DOI: 10.1098/rsif.2022.0182] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Recent work has highlighted the possibility of 'rate-induced tipping', in which a system undergoes an abrupt transition when a perturbation exceeds a critical rate of change. Here, we argue that this is widely applicable to evolutionary systems: collapse, or extinction, may occur when external changes occur too fast for evolutionary adaptation to keep up. To bridge existing theoretical frameworks, we develop a minimal evolutionary-ecological model showing that rate-induced extinction and the established notion of 'evolutionary rescue' are fundamentally two sides of the same coin: the failure of one implies the other, and vice versa. We compare the minimal model's behaviour with that of a more complex model in which the large-scale dynamics emerge from the interactions of many individual agents; in both cases, there is a well-defined threshold rate to induce extinction, and a consistent scaling law for that rate as a function of timescale. Due to the fundamental nature of the underlying mechanism, we suggest that a vast range of evolutionary systems should in principle be susceptible to rate-induced collapse. This would include ecosystems on all scales as well as human societies; further research is warranted.
Collapse
Affiliation(s)
- Constantin W Arnscheidt
- Lorenz Center, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Daniel H Rothman
- Lorenz Center, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA
| |
Collapse
|
43
|
Gupta S, Mastrantonas N, Masoller C, Kurths J. Perspectives on the importance of complex systems in understanding our climate and climate change-The Nobel Prize in Physics 2021. CHAOS (WOODBURY, N.Y.) 2022; 32:052102. [PMID: 35649980 DOI: 10.1063/5.0090222] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 04/27/2022] [Indexed: 06/15/2023]
Abstract
The Nobel Prize in Physics 2021 was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their "groundbreaking contributions to our understanding of complex systems," including major advances in the understanding of our climate and climate change. In this Perspective article, we review their key contributions and discuss their relevance in relation to the present understanding of our climate. We conclude by outlining some promising research directions and open questions in climate science.
Collapse
Affiliation(s)
- Shraddha Gupta
- Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Telegrafenberg A56, Potsdam 14473, Germany
| | - Nikolaos Mastrantonas
- European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading RG2 9AX, United Kingdom
| | - Cristina Masoller
- Departament de Física, Universitat Politecnica de Catalunya, Sant Nebridi 22, 08222 Terrassa, Spain
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research (PIK)-Member of the Leibniz Association, Telegrafenberg A56, Potsdam 14473, Germany
| |
Collapse
|
44
|
van Belzen J, Fivash GS, Hu Z, Bouma TJ, Herman PMJ. A probabilistic framework for windows of opportunity: the role of temporal variability in critical transitions. J R Soc Interface 2022; 19:20220041. [PMID: 35506213 PMCID: PMC9065964 DOI: 10.1098/rsif.2022.0041] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2022] [Accepted: 04/04/2022] [Indexed: 11/13/2022] Open
Abstract
The establishment of young organisms in harsh environments often requires a window of opportunity (WoO). That is, a short time window in which environmental conditions drop long enough below the hostile average level, giving the organism time to develop tolerance and transition into stable existence. It has been suggested that this kind of establishment dynamics is a noise-induced transition between two alternate states. Understanding how temporal variability (i.e. noise) in environmental conditions affects establishment of organisms is therefore key, yet not well understood or included explicitly in the WoO framework. In this paper, we develop a coherent theoretical framework for understanding when the WoO open or close based on simple dichotomous environmental variation. We reveal that understanding of the intrinsic timescales of both the developing organism and the environment is fundamental to predict if organisms can or cannot establish. These insights have allowed us to develop statistical laws for predicting establishment probabilities based on the period and variance of the fluctuations in naturally variable environments. Based on this framework, we now get a clear understanding of how changes in the timing and magnitude of climate variability or management can mediate establishment chances.
Collapse
Affiliation(s)
- Jim van Belzen
- Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research (NIOZ), 4401 NT Yerseke, The Netherlands
| | - Gregory S. Fivash
- Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research (NIOZ), 4401 NT Yerseke, The Netherlands
| | - Zhan Hu
- School of Marine Sciences, Sun Yat-Sen University, and Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai, People's Republic of China
- Guangdong Provincial Key Laboratory of Marine Resources and Coastal Engineering, Guangzhou, People's Republic of China
- Pearl River Estuary Marine Ecosystem Research Station, Ministry of Education, Zhuhai, People's Republic of China
| | - Tjeerd J. Bouma
- Department of Estuarine and Delta Systems, Royal Netherlands Institute for Sea Research (NIOZ), 4401 NT Yerseke, The Netherlands
- Faculty of Geosciences, Department of Physical Geography, Utrecht University, 3508 TC Utrecht, The Netherlands
| | - Peter M. J. Herman
- Department of Hydraulic Engineering, Delft University of Technology, 2628 CN, Delft, The Netherlands
- Unit of Marine and Coastal Systems, Deltares, 2600 MH, Delft, The Netherlands
| |
Collapse
|
45
|
Kuehn C, Lux K, Neamţu A. Warning signs for non-Markovian bifurcations: colour blindness and scaling laws. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0740] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Warning signs for tipping points (or critical transitions) have been very actively studied. Although the theory has been applied successfully in models and in experiments for many complex systems such as for tipping in climate systems, there are ongoing debates as to when warning signs can be extracted from data. In this work, we shed light on this debate by considering different types of underlying noise. Thereby, we significantly advance the general theory of warning signs for nonlinear stochastic dynamics. A key scenario deals with stochastic systems approaching a bifurcation point dynamically upon slow parameter variation. The stochastic fluctuations are generically able to probe the dynamics near a deterministic attractor to reveal critical slowing down. Using scaling laws near bifurcations, one can then anticipate the distance to a bifurcation. Previous warning signs results assume that the noise is Markovian, most often even white. Here, we study warning signs for non-Markovian systems including coloured noise and
α
-regular Volterra processes (of which fractional Brownian motion and the Rosenblatt process are special cases). We prove that early warning scaling laws can disappear completely or drastically change their exponent based upon the parameters controlling the noise process. This provides a clear explanation as to why applying standard warning signs results to reduced models of complex systems may not agree with data-driven studies. We demonstrate our results numerically in the context of a box model of the Atlantic Meridional Overturning Circulation.
Collapse
Affiliation(s)
- Christian Kuehn
- Department of Mathematics, Technical University of Munich, Boltzmannstr. 3, Garching b. München 85748, Germany
- Complexity Science Hub Vienna, Josefstädter Str. 39, Vienna 1080, Austria
| | - Kerstin Lux
- Department of Mathematics, Technical University of Munich, Boltzmannstr. 3, Garching b. München 85748, Germany
| | - Alexandra Neamţu
- Department of Mathematics and Statistics, University of Konstanz, Universitätsstr. 10, Konstanz 78464, Germany
| |
Collapse
|
46
|
Proverbio D, Kemp F, Magni S, Gonçalves J. Performance of early warning signals for disease re-emergence: A case study on COVID-19 data. PLoS Comput Biol 2022; 18:e1009958. [PMID: 35353809 PMCID: PMC9000113 DOI: 10.1371/journal.pcbi.1009958] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Revised: 04/11/2022] [Accepted: 02/23/2022] [Indexed: 01/12/2023] Open
Abstract
Developing measures for rapid and early detection of disease re-emergence is important to perform science-based risk assessment of epidemic threats. In the past few years, several early warning signals (EWS) from complex systems theory have been introduced to detect impending critical transitions and extend the set of indicators. However, it is still debated whether they are generically applicable or potentially sensitive to some dynamical characteristics such as system noise and rates of approach to critical parameter values. Moreover, testing on empirical data has, so far, been limited. Hence, verifying EWS performance remains a challenge. In this study, we tackle this question by analyzing the performance of common EWS, such as increasing variance and autocorrelation, in detecting the emergence of COVID-19 outbreaks in various countries. Our work illustrates that these EWS might be successful in detecting disease emergence when some basic assumptions are satisfied: a slow forcing through the transitions and not-fat-tailed noise. In uncertain cases, we observe that noise properties or commensurable time scales may obscure the expected early warning signals. Overall, our results suggest that EWS can be useful for active monitoring of epidemic dynamics, but that their performance is sensitive to certain features of the underlying dynamics. Our findings thus pave a connection between theoretical and empirical studies, constituting a further step towards the application of EWS indicators for informing public health policies.
Collapse
Affiliation(s)
- Daniele Proverbio
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux, Luxembourg
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom
| | - Françoise Kemp
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux, Luxembourg
| | - Stefano Magni
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux, Luxembourg
| | - Jorge Gonçalves
- Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux, Luxembourg
- Department of Plant Sciences, University of Cambridge, Cambridge, United Kingdom
| |
Collapse
|
47
|
Cenedese M, Axås J, Bäuerlein B, Avila K, Haller G. Data-driven modeling and prediction of non-linearizable dynamics via spectral submanifolds. Nat Commun 2022; 13:872. [PMID: 35169152 PMCID: PMC8847615 DOI: 10.1038/s41467-022-28518-y] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Accepted: 01/25/2022] [Indexed: 11/25/2022] Open
Abstract
We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with finitely many frequencies. Our data-driven, sparse, nonlinear models are obtained as extended normal forms of the reduced dynamics on low-dimensional, attracting spectral submanifolds (SSMs) of the dynamical system. We illustrate the power of data-driven SSM reduction on high-dimensional numerical data sets and experimental measurements involving beam oscillations, vortex shedding and sloshing in a water tank. We find that SSM reduction trained on unforced data also predicts nonlinear response accurately under additional external forcing.
Collapse
Affiliation(s)
- Mattia Cenedese
- Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092, Zürich, Switzerland
| | - Joar Axås
- Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092, Zürich, Switzerland
| | - Bastian Bäuerlein
- University of Bremen, Faculty of Production Engineering, Badgasteiner Strasse 1, 28359, Bremen, Germany
- Leibniz Institute for Materials Engineering IWT, Badgasteiner Strasse 3, 28359, Bremen, Germany
| | - Kerstin Avila
- University of Bremen, Faculty of Production Engineering, Badgasteiner Strasse 1, 28359, Bremen, Germany
- Leibniz Institute for Materials Engineering IWT, Badgasteiner Strasse 3, 28359, Bremen, Germany
| | - George Haller
- Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092, Zürich, Switzerland.
| |
Collapse
|
48
|
Abstract
The ancient idea of the balance of nature continues to influence modern perspectives on global environmental change. Assumptions of stable biogeochemical steady states and linear responses to perturbation are widely employed in the interpretation of geochemical records. Here, we review the dynamics of the marine carbon cycle and its interactions with climate and life over geologic time, focusing on what the record of past changes can teach us about stability and instability in the Earth system. Emerging themes include the role of amplifying feedbacks in producing past carbon cycle disruptions, the importance of critical rates of change in the context of mass extinctions and potential Earth system tipping points, and the application of these ideas to the modern unbalanced carbon cycle. A comprehensive dynamical understanding of the marine record of global environmental disruption will be of great value in understanding the long-term consequences of anthropogenic change.
Collapse
Affiliation(s)
- Constantin W Arnscheidt
- Lorenz Center, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; ,
| | - Daniel H Rothman
- Lorenz Center, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA; ,
| |
Collapse
|
49
|
Fischer T, Rings T, Rahimi Tabar MR, Lehnertz K. Towards a Data-Driven Estimation of Resilience in Networked Dynamical Systems: Designing a Versatile Testbed. FRONTIERS IN NETWORK PHYSIOLOGY 2022; 2:838142. [PMID: 36926066 PMCID: PMC10013011 DOI: 10.3389/fnetp.2022.838142] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2021] [Accepted: 02/03/2022] [Indexed: 11/13/2022]
Abstract
Estimating resilience of adaptive, networked dynamical systems remains a challenge. Resilience refers to a system's capacity "to absorb exogenous and/or endogenous disturbances and to reorganize while undergoing change so as to still retain essentially the same functioning, structure, and feedbacks." The majority of approaches to estimate resilience requires exact knowledge of the underlying equations of motion; the few data-driven approaches so far either lack appropriate strategies to verify their suitability or remain subject of considerable debate. We develop a testbed that allows one to modify resilience of a multistable networked dynamical system in a controlled manner. The testbed also enables generation of multivariate time series of system observables to evaluate the suitability of data-driven estimators of resilience. We report first findings for such an estimator.
Collapse
Affiliation(s)
- Tobias Fischer
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany
| | - M Reza Rahimi Tabar
- Department of Physics, Sharif University of Technology, Tehran, Iran.,Institute of Physics, Carl von Ossietzky University of Oldenburg, Oldenburg, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Bonn, Germany.,Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Bonn, Germany.,Interdisciplinary Center for Complex Systems, University of Bonn, Bonn, Germany
| |
Collapse
|
50
|
Abstract
AbstractThe transformation of ecosystems proceeds at unprecedented rates. Recent studies suggest that high rates of environmental change can cause rate-induced tipping. In ecological models, the associated rate-induced critical transition manifests during transient dynamics in which populations drop to dangerously low densities. In this work, we study how indirect evolutionary rescue—due to the rapid evolution of a predator’s trait—can save a prey population from the rate-induced collapse. Therefore, we explicitly include the time-dependent dynamics of environmental change and evolutionary adaptation in an eco-evolutionary system. We then examine how fast the evolutionary adaptation needs to be to counteract the response to environmental degradation and express this relationship by means of a critical rate. Based on this critical rate, we conclude that indirect evolutionary rescue is more probable if the predator population possesses a high genetic variation and, simultaneously, the environmental change is slow. Hence, our results strongly emphasize that the maintenance of biodiversity requires a deceleration of the anthropogenic degradation of natural habitats.
Collapse
|