1
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Gentili PL, Stano P. Living cells and biological mechanisms as prototypes for developing chemical artificial intelligence. Biochem Biophys Res Commun 2024; 720:150060. [PMID: 38754164 DOI: 10.1016/j.bbrc.2024.150060] [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: 10/26/2023] [Revised: 03/25/2024] [Accepted: 05/06/2024] [Indexed: 05/18/2024]
Abstract
Artificial Intelligence (AI) is having a revolutionary impact on our societies. It is helping humans in facing the global challenges of this century. Traditionally, AI is developed in software or through neuromorphic engineering in hardware. More recently, a brand-new strategy has been proposed. It is the so-called Chemical AI (CAI), which exploits molecular, supramolecular, and systems chemistry in wetware to mimic human intelligence. In this work, two promising approaches for boosting CAI are described. One regards designing and implementing neural surrogates that can communicate through optical or chemical signals and give rise to networks for computational purposes and to develop micro/nanorobotics. The other approach concerns "bottom-up synthetic cells" that can be exploited for applications in various scenarios, including future nano-medicine. Both topics are presented at a basic level, mainly to inform the broader audience of non-specialists, and so favour the rise of interest in these frontier subjects.
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Affiliation(s)
- Pier Luigi Gentili
- Department of Chemistry, Biology, and Biotechnology, Università degli Studi di Perugia, Perugia, Italy.
| | - Pasquale Stano
- Department of Biological and Environmental Sciences and Technologies (DiSTeBA), University of Salento, Lecce, Italy.
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2
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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.
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3
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Bi MX, Fan H, Yan XH, Lai YC. Folding State within a Hysteresis Loop: Hidden Multistability in Nonlinear Physical Systems. PHYSICAL REVIEW LETTERS 2024; 132:137201. [PMID: 38613259 DOI: 10.1103/physrevlett.132.137201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/25/2023] [Revised: 11/28/2023] [Accepted: 02/12/2024] [Indexed: 04/14/2024]
Abstract
Identifying hidden states in nonlinear physical systems that evade direct experimental detection is important as disturbances and noises can place the system in a hidden state with detrimental consequences. We study a cavity magnonic system whose main physics is photon and magnon Kerr effects. Sweeping a bifurcation parameter in numerical experiments (as would be done in actual experiments) leads to a hysteresis loop with two distinct stable steady states, but analytic calculation gives a third folded steady state "hidden" in the loop, which gives rise to the phenomenon of hidden multistability. We propose an experimentally feasible control method to drive the system into the folded hidden state. We demonstrate, through a ternary cavity magnonic system and a gene regulatory network, that such hidden multistability is in fact quite common. Our findings shed light on hidden dynamical states in nonlinear physical systems which are not directly observable but can present challenges and opportunities in applications.
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Affiliation(s)
- Meng-Xia Bi
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Huawei Fan
- School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
| | - Xiao-Hong Yan
- School of Material Science and Engineering, Jiangsu University, Zhenjiang 212013, China
| | - Ying-Cheng Lai
- School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
- Department of Physics, Arizona State University, Tempe, Arizona 85287, USA
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4
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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.
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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
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5
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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.
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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
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6
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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.
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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
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7
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Cannarsa P, Lucarini V, Martinez P, Urbani C, Vancostenoble J. Analysis of a two-layer energy balance model: Long time behavior and greenhouse effect. CHAOS (WOODBURY, N.Y.) 2023; 33:113111. [PMID: 37930684 DOI: 10.1063/5.0136673] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2022] [Accepted: 10/06/2023] [Indexed: 11/07/2023]
Abstract
We study a two-layer energy balance model that allows for vertical exchanges between a surface layer and the atmosphere. The evolution equations of the surface temperature and the atmospheric temperature are coupled by the emission of infrared radiation by one level, that emission being partly captured by the other layer, and the effect of all non-radiative vertical exchanges of energy. Therefore, an essential parameter is the absorptivity of the atmosphere, denoted εa. The value of εa depends critically on greenhouse gases: increasing concentrations of CO2 and CH4 lead to a more opaque atmosphere with higher values of ϵa. First, we prove that global existence of solutions of the system holds if and only if εa∈(0,2) and blow up in finite time occurs if εa>2. (Note that the physical range of values for εa is (0,1].) Next, we explain the long time dynamics for εa∈(0,2), and we prove that all solutions converge to some equilibrium point. Finally, motivated by the physical context, we study the dependence of the equilibrium points with respect to the involved parameters, and we prove, in particular, that the surface temperature increases monotonically with respect to εa. This is the key mathematical manifestation of the greenhouse effect.
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Affiliation(s)
- P Cannarsa
- Dipartimento degli Studi di Matematica, Università di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma, Italy
| | - V Lucarini
- Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, United Kingdom and Centre for the Mathematics of Planet Earth, University of Reading, Reading RG6 6AX, United Kingdom
| | - P Martinez
- Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse; CNRS UPS IMT, F-31062 Toulouse Cedex 9, France
| | - C Urbani
- Dipartimento di Scienze Tecnologiche e dell'Innovazione, Università Mercatorum, Piazza Mattei 10, 00186 Roma, Italy
| | - J Vancostenoble
- Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse; CNRS UPS IMT, F-31062 Toulouse Cedex 9, France
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8
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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.
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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
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9
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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.
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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
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Patel D, Ott E. Using machine learning to anticipate tipping points and extrapolate to post-tipping dynamics of non-stationary dynamical systems. CHAOS (WOODBURY, N.Y.) 2023; 33:023143. [PMID: 36859201 DOI: 10.1063/5.0131787] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/24/2022] [Accepted: 01/31/2023] [Indexed: 06/18/2023]
Abstract
The ability of machine learning (ML) models to "extrapolate" to situations outside of the range spanned by their training data is crucial for predicting the long-term behavior of non-stationary dynamical systems (e.g., prediction of terrestrial climate change), since the future trajectories of such systems may (perhaps after crossing a tipping point) explore regions of state space which were not explored in past time-series measurements used as training data. We investigate the extent to which ML methods can yield useful results by extrapolation of such training data in the task of forecasting non-stationary dynamics, as well as conditions under which such methods fail. In general, we find that ML can be surprisingly effective even in situations that might appear to be extremely challenging, but do (as one would expect) fail when "too much" extrapolation is required. For the latter case, we show that good results can potentially be obtained by combining the ML approach with an available inaccurate conventional model based on scientific knowledge.
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Affiliation(s)
- Dhruvit Patel
- The Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 26742, USA
| | - Edward Ott
- The Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 26742, USA
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11
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Lea-Carnall CA, Tanner LI, Montemurro MA. Noise-modulated multistable synapses in a Wilson-Cowan-based model of plasticity. Front Comput Neurosci 2023; 17:1017075. [PMID: 36817317 PMCID: PMC9931909 DOI: 10.3389/fncom.2023.1017075] [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: 08/12/2022] [Accepted: 01/10/2023] [Indexed: 02/05/2023] Open
Abstract
Frequency-dependent plasticity refers to changes in synaptic strength in response to different stimulation frequencies. Resonance is a factor known to be of importance in such frequency dependence, however, the role of neural noise in the process remains elusive. Considering the brain is an inherently noisy system, understanding its effects may prove beneficial in shaping therapeutic interventions based on non-invasive brain stimulation protocols. The Wilson-Cowan (WC) model is a well-established model to describe the average dynamics of neural populations and has been shown to exhibit bistability in the presence of noise. However, the important question of how the different stable regimes in the WC model can affect synaptic plasticity when cortical populations interact has not yet been addressed. Therefore, we investigated plasticity dynamics in a WC-based model of interacting neural populations coupled with activity-dependent synapses in which a periodic stimulation was applied in the presence of noise of controlled intensity. The results indicate that for a narrow range of the noise variance, synaptic strength can be optimized. In particular, there is a regime of noise intensity for which synaptic strength presents a triple-stable state. Regulating noise intensity affects the probability that the system chooses one of the stable states, thereby controlling plasticity. These results suggest that noise is a highly influential factor in determining the outcome of plasticity induced by stimulation.
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Affiliation(s)
- Caroline A Lea-Carnall
- School of Health Sciences, Manchester Academic Health Science Centre, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Lisabel I Tanner
- School of Health Sciences, Manchester Academic Health Science Centre, Faculty of Biology, Medicine and Health, University of Manchester, Manchester, United Kingdom
| | - Marcelo A Montemurro
- School of Mathematics and Statistics, Faculty of Science, Technology, Engineering and Mathematics, The Open University, Milton Keynes, United Kingdom
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12
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Roy M, Mandal S, Hens C, Prasad A, Kuznetsov NV, Dev Shrimali M. Model-free prediction of multistability using echo state network. CHAOS (WOODBURY, N.Y.) 2022; 32:101104. [PMID: 36319300 DOI: 10.1063/5.0119963] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2022] [Accepted: 09/20/2022] [Indexed: 06/16/2023]
Abstract
In the field of complex dynamics, multistable attractors have been gaining significant attention due to their unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance and ecological to social systems. In this article, we investigate a data-driven approach to infer different dynamics of a multistable system using an echo state network. We start with a parameter-aware reservoir and predict diverse dynamics for different parameter values. Interestingly, a machine is able to reproduce the dynamics almost perfectly even at distant parameters, which lie considerably far from the parameter values related to the training dynamics. In continuation, we can predict whole bifurcation diagram significant accuracy as well. We extend this study for exploring various dynamics of multistable attractors at an unknown parameter value. While we train the machine with the dynamics of only one attractor at parameter p, it can capture the dynamics of a co-existing attractor at a new parameter value p + Δ p. Continuing the simulation for a multiple set of initial conditions, we can identify the basins for different attractors. We generalize the results by applying the scheme on two distinct multistable systems.
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Affiliation(s)
- Mousumi Roy
- Department of Physics, Central University of Rajasthan, Ajmer 305817, Rajasthan, India
| | - Swarnendu Mandal
- Department of Physics, Central University of Rajasthan, Ajmer 305817, Rajasthan, India
| | - Chittaranjan Hens
- Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology, Gachibowli, Hyderabad 500032, India
| | - Awadhesh Prasad
- Department of Physics & Astrophysics, University of Delhi, Delhi 110007, India
| | - N V Kuznetsov
- Department of Applied Cybernetics, Saint Petersburg University, St. Petersburg 198504, Russia
| | - Manish Dev Shrimali
- Department of Physics, Central University of Rajasthan, Ajmer 305817, Rajasthan, India
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13
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Meucci R, Marc Ginoux J, Mehrabbeik M, Jafari S, Clinton Sprott J. Generalized multistability and its control in a laser. CHAOS (WOODBURY, N.Y.) 2022; 32:083111. [PMID: 36049920 DOI: 10.1063/5.0093727] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 05/09/2022] [Indexed: 06/15/2023]
Abstract
We revisit the laser model with cavity loss modulation, from which evidence of chaos and generalized multistability was discovered in 1982. Multistability refers to the coexistence of two or more attractors in nonlinear dynamical systems. Despite its relative simplicity, the adopted model shows us how the multistability depends on the dissipation of the system. The model is then tested under the action of a secondary sinusoidal perturbation, which can remove bistability when a suitable relative phase is chosen. The surviving attractor is the one with less dissipation. This control strategy is particularly useful when one of the competing attractors is a chaotic attractor.
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Affiliation(s)
- Riccardo Meucci
- Istituto Nazionale di Ottica-CNR, Largo E. Fermi 6, 50125 Firenze, Italy
| | - Jean Marc Ginoux
- Laboratoire CPT, Université de Toulon, CS 60584, 83041 Toulon Cedex 9, France
| | - Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Julien Clinton Sprott
- Department of Physics, University of Wisconsin, 1150 University Avenue Madison, Madison, Wisconsin 53706-1390, USA
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Datseris G, Wagemakers A. Effortless estimation of basins of attraction. CHAOS (WOODBURY, N.Y.) 2022; 32:023104. [PMID: 35232033 DOI: 10.1063/5.0076568] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2021] [Accepted: 01/11/2022] [Indexed: 06/14/2023]
Abstract
We present a fully automated method that identifies attractors and their basins of attraction without approximations of the dynamics. The method works by defining a finite state machine on top of the dynamical system flow. The input to the method is a dynamical system evolution rule and a grid that partitions the state space. No prior knowledge of the number, location, or nature of the attractors is required. The method works for arbitrarily high-dimensional dynamical systems, both discrete and continuous. It also works for stroboscopic maps, Poincaré maps, and projections of high-dimensional dynamics to a lower-dimensional space. The method is accompanied by a performant open-source implementation in the DynamicalSystems.jl library. The performance of the method outclasses the naïve approach of evolving initial conditions until convergence to an attractor, even when excluding the task of first identifying the attractors from the comparison. We showcase the power of our implementation on several scenarios, including interlaced chaotic attractors, high-dimensional state spaces, fractal basin boundaries, and interlaced attracting periodic orbits, among others. The output of our method can be straightforwardly used to calculate concepts, such as basin stability and final state sensitivity.
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Affiliation(s)
- George Datseris
- Max Planck Institute for Meteorology, 20146 Hamburg, Germany
| | - Alexandre Wagemakers
- Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles 28933, Madrid, Tulipán s/n, Spain
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15
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Newman J, Lucas M, Stefanovska A. Stabilization of cyclic processes by slowly varying forcing. CHAOS (WOODBURY, N.Y.) 2021; 31:123129. [PMID: 34972346 DOI: 10.1063/5.0066641] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Accepted: 10/22/2021] [Indexed: 06/14/2023]
Abstract
We introduce a new mathematical framework for the qualitative analysis of dynamical stability, designed particularly for finite-time processes subject to slow-timescale external influences. In particular, our approach is to treat finite-time dynamical systems in terms of a slow-fast formalism in which the slow time only exists in a bounded interval, and consider stability in the singular limit. Applying this to one-dimensional phase dynamics, we provide stability definitions somewhat analogous to the classical infinite-time definitions associated with Aleksandr Lyapunov. With this, we mathematically formalize and generalize a phase-stabilization phenomenon previously described in the physics literature for which the classical stability definitions are inapplicable and instead our new framework is required.
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Affiliation(s)
- J Newman
- Centre for Systems, Dynamics and Control, Department of Mathematics, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - M Lucas
- Dipartimento di Fisica e Astronomia, Università di Firenze, INFN and CSDC, Via Sansone 1, 50019 Sesto Fiorentino, Firenze, Italy
| | - A Stefanovska
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
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16
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Kohler J, Wunderling N, Donges JF, Vollmer J. Complex networks of interacting stochastic tipping elements: Cooperativity of phase separation in the large-system limit. Phys Rev E 2021; 104:044301. [PMID: 34781496 DOI: 10.1103/physreve.104.044301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 08/26/2021] [Indexed: 11/07/2022]
Abstract
Tipping elements in the Earth system have received increased scientific attention over recent years due to their nonlinear behavior and the risks of abrupt state changes. While being stable over a large range of parameters, a tipping element undergoes a drastic shift in its state upon an additional small parameter change when close to its tipping point. Recently, the focus of research broadened towards emergent behavior in networks of tipping elements, like global tipping cascades triggered by local perturbations. Here, we analyze the response to the perturbation of a single node in a system that initially resides in an unstable equilibrium. The evolution is described in terms of coupled nonlinear equations for the cumulants of the distribution of the elements. We show that drift terms acting on individual elements and offsets in the coupling strength are subdominant in the limit of large networks, and we derive an analytical prediction for the evolution of the expectation (i.e., the first cumulant). It behaves like a single aggregated tipping element characterized by a dimensionless parameter that accounts for the network size, its overall connectivity, and the average coupling strength. The resulting predictions are in excellent agreement with numerical data for Erdös-Rényi, Barabási-Albert, and Watts-Strogatz networks of different size and with different coupling parameters.
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Affiliation(s)
- Jan Kohler
- Institute for Theoretical Physics, University of Leipzig, 04103 Leipzig, Germany, EU.,Earth System Analysis, Potsdam-Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany, EU
| | - Nico Wunderling
- Earth System Analysis, Potsdam-Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany, EU.,Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany, EU.,Department of Physics, Humboldt University of Berlin, 12489 Berlin, Germany, EU
| | - Jonathan F Donges
- Earth System Analysis, Potsdam-Institute for Climate Impact Research, Member of the Leibniz Association, 14473 Potsdam, Germany, EU.,Stockholm Resilience Centre, Stockholm University, 10691 Stockholm, Sweden, EU
| | - Jürgen Vollmer
- Institute for Theoretical Physics, University of Leipzig, 04103 Leipzig, Germany, EU
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17
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A trajectory-based loss function to learn missing terms in bifurcating dynamical systems. Sci Rep 2021; 11:20394. [PMID: 34650131 PMCID: PMC8516982 DOI: 10.1038/s41598-021-99609-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2021] [Accepted: 09/21/2021] [Indexed: 11/15/2022] Open
Abstract
Missing terms in dynamical systems are a challenging problem for modeling. Recent developments in the combination of machine learning and dynamical system theory open possibilities for a solution. We show how physics-informed differential equations and machine learning—combined in the Universal Differential Equation (UDE) framework by Rackauckas et al.—can be modified to discover missing terms in systems that undergo sudden fundamental changes in their dynamical behavior called bifurcations. With this we enable the application of the UDE approach to a wider class of problems which are common in many real world applications. The choice of the loss function, which compares the training data trajectory in state space and the current estimated solution trajectory of the UDE to optimize the solution, plays a crucial role within this approach. The Mean Square Error as loss function contains the risk of a reconstruction which completely misses the dynamical behavior of the training data. By contrast, our suggested trajectory-based loss function which optimizes two largely independent components, the length and angle of state space vectors of the training data, performs reliable well in examples of systems from neuroscience, chemistry and biology showing Saddle-Node, Pitchfork, Hopf and Period-doubling bifurcations.
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18
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Bragard J, Witt A, Laroze D, Hawks C, Elorza J, Rodríguez Cantalapiedra I, Peñaranda A, Echebarria B. Conductance heterogeneities induced by multistability in the dynamics of coupled cardiac gap junctions. CHAOS (WOODBURY, N.Y.) 2021; 31:073144. [PMID: 34340360 DOI: 10.1063/5.0053651] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Accepted: 07/08/2021] [Indexed: 06/13/2023]
Abstract
In this paper, we study the propagation of the cardiac action potential in a one-dimensional fiber, where cells are electrically coupled through gap junctions (GJs). We consider gap junctional gate dynamics that depend on the intercellular potential. We find that different GJs in the tissue can end up in two different states: a low conducting state and a high conducting state. We first present evidence of the dynamical multistability that occurs by setting specific parameters of the GJ dynamics. Subsequently, we explain how the multistability is a direct consequence of the GJ stability problem by reducing the dynamical system's dimensions. The conductance dispersion usually occurs on a large time scale, i.e., thousands of heartbeats. The full cardiac model simulations are computationally demanding, and we derive a simplified model that allows for a reduction in the computational cost of four orders of magnitude. This simplified model reproduces nearly quantitatively the results provided by the original full model. We explain the discrepancies between the two models due to the simplified model's lack of spatial correlations. This simplified model provides a valuable tool to explore cardiac dynamics over very long time scales. That is highly relevant in studying diseases that develop on a large time scale compared to the basic heartbeat. As in the brain, plasticity and tissue remodeling are crucial parameters in determining the action potential wave propagation's stability.
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Affiliation(s)
- J Bragard
- Departamento de Física y Matemática Aplicada, Universidad de Navarra, Pamplona 31080, Spain
| | - A Witt
- Max-Planck Institute, Gottingen 37077, Germany
| | - D Laroze
- Instituto de Alta Investigación, CEDENNA, Universidad de Tarapacá, Casilla 7D, Arica, Chile
| | - C Hawks
- Departamento de Física y Matemática Aplicada, Universidad de Navarra, Pamplona 31080, Spain
| | - J Elorza
- Departamento de Física y Matemática Aplicada, Universidad de Navarra, Pamplona 31080, Spain
| | | | - A Peñaranda
- Departament de Física, Universitat Politècnica de Catalunya, Barcelona 08068, Spain
| | - B Echebarria
- Departament de Física, Universitat Politècnica de Catalunya, Barcelona 08068, Spain
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19
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Pierini S, Ghil M. Tipping points induced by parameter drift in an excitable ocean model. Sci Rep 2021; 11:11126. [PMID: 34045519 PMCID: PMC8159979 DOI: 10.1038/s41598-021-90138-1] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2020] [Accepted: 04/26/2021] [Indexed: 11/09/2022] Open
Abstract
Numerous systems in the climate sciences and elsewhere are excitable, exhibiting coexistence of and transitions between a basic and an excited state. We examine the role of tipping between two such states in an excitable low-order ocean model. Ensemble simulations are used to obtain the model's pullback attractor (PBA) and its properties, as a function of a forcing parameter [Formula: see text] and of the steepness [Formula: see text] of a climatological drift in the forcing. The tipping time [Formula: see text] is defined as the time at which the transition to relaxation oscillations (ROs) arises: at constant forcing this occurs at [Formula: see text]. As the steepness [Formula: see text] decreases, [Formula: see text] is delayed and the corresponding forcing amplitude decreases, while remaining always above [Formula: see text]. With periodic perturbations, that amplitude depends solely on [Formula: see text] over a significant range of parameters: this provides an example of rate-induced tipping in an excitable system. Nonlinear resonance occurs for periods comparable to the RO time scale. Coexisting PBAs and total independence from initial states are found for subsets of parameter space. In the broader context of climate dynamics, the parameter drift herein stands for the role of anthropogenic forcing.
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Affiliation(s)
- Stefano Pierini
- Department of Science and Technology, Parthenope University of Naples, Centro Direzionale, Isola C4, 80143, Napoli, Italy. .,CoNISMa, Rome, Italy.
| | - Michael Ghil
- Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), École Normale Supérieure and PSL University, Paris, France.,Atmospheric and Oceanic Sciences Department, University of California at Los Angeles, Los Angeles, CA, USA
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20
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Schoenmakers S, Feudel U. A resilience concept based on system functioning: A dynamical systems perspective. CHAOS (WOODBURY, N.Y.) 2021; 31:053126. [PMID: 34240958 DOI: 10.1063/5.0042755] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/03/2021] [Accepted: 04/21/2021] [Indexed: 06/13/2023]
Abstract
We introduce a new framework for resilience, which is traditionally understood as the ability of a system to absorb disturbances and maintain its state, by proposing a shift from a state-based to a system functioning-based approach to resilience, which takes into account that several different coexisting stable states could fulfill the same functioning. As a consequence, not every regime shift, i.e., transition from one stable state to another, is associated with a lack or loss of resilience. We emphasize the importance of flexibility-the ability of a system to shift between different stable states while still maintaining system functioning. Furthermore, we provide a classification of system responses based on the phenomenological properties of possible disturbances, including the role of their timescales. Therefore, we discern fluctuations, shocks, press disturbances, and trends as possible disturbances. We distinguish between two types of mechanisms of resilience: (i) tolerance and flexibility, which are properties of the system, and (ii) adaptation and transformation, which are processes that alter the system's tolerance and flexibility. Furthermore, we discuss quantitative methods to investigate resilience in model systems based on approaches developed in dynamical systems theory.
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Affiliation(s)
- Sarah Schoenmakers
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, 26111 Oldenburg, Germany
| | - Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, Carl von Ossietzky University of Oldenburg, 26111 Oldenburg, Germany
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21
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Bhandary S, Kaur T, Banerjee T, Dutta PS. Network resilience of FitzHugh-Nagumo neurons in the presence of nonequilibrium dynamics. Phys Rev E 2021; 103:022314. [PMID: 33736003 DOI: 10.1103/physreve.103.022314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2020] [Accepted: 02/01/2021] [Indexed: 11/07/2022]
Abstract
Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the face of perturbations. Most of the research on network resilience has focused on the transition from one equilibrium state to an alternative equilibrium state. Although the presence of nonequilibrium dynamics in some nodes may advance or delay sudden transitions in networks and give early warning signals of an impending collapse, it has not been studied much in the context of network resilience. Here we bridge this gap by studying a neuronal network model with diverse topologies, in which nonequilibrium dynamics may appear in the network even before the transition to a resting state from an active state in response to environmental stress deteriorating their external conditions. We find that the percentage of uncoupled nodes exhibiting nonequilibrium dynamics plays a vital role in determining the network's transition type. We show that a higher proportion of nodes with nonequilibrium dynamics can delay the tipping and increase networks' resilience against environmental stress, irrespective of their topology. Further, predictability of an upcoming transition weakens, as the network topology moves from regular to disordered.
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Affiliation(s)
- Subhendu Bhandary
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
| | - Taranjot Kaur
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
| | - Tanmoy Banerjee
- Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan 713 104, West Bengal, India
| | - Partha Sharathi Dutta
- Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India
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22
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Gross T. Not One, but Many Critical States: A Dynamical Systems Perspective. Front Neural Circuits 2021; 15:614268. [PMID: 33737868 PMCID: PMC7960911 DOI: 10.3389/fncir.2021.614268] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2020] [Accepted: 02/05/2021] [Indexed: 02/01/2023] Open
Abstract
The past decade has seen growing support for the critical brain hypothesis, i.e., the possibility that the brain could operate at or very near a critical state between two different dynamical regimes. Such critical states are well-studied in different disciplines, therefore there is potential for a continued transfer of knowledge. Here, I revisit foundations of bifurcation theory, the mathematical theory of transitions. While the mathematics is well-known it's transfer to neural dynamics leads to new insights and hypothesis.
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Affiliation(s)
- Thilo Gross
- Helmholtz Institute for Functional Marine Biodiversity (HIFMB), Oldenburg, Germany
- Institute for Chemistry and Biology of the Marine Environment (ICBM), Carl-von-Ossietzky Universität Oldenburg, Oldenburg, Germany
- Helmholtz Center for Marine and Polar Research, Alfred-Wegener-Institute, Bremerhaven, Germany
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23
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Rombouts J, Gelens L. Dynamic bistable switches enhance robustness and accuracy of cell cycle transitions. PLoS Comput Biol 2021; 17:e1008231. [PMID: 33411761 PMCID: PMC7817062 DOI: 10.1371/journal.pcbi.1008231] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Revised: 01/20/2021] [Accepted: 11/18/2020] [Indexed: 02/06/2023] Open
Abstract
Bistability is a common mechanism to ensure robust and irreversible cell cycle transitions. Whenever biological parameters or external conditions change such that a threshold is crossed, the system abruptly switches between different cell cycle states. Experimental studies have uncovered mechanisms that can make the shape of the bistable response curve change dynamically in time. Here, we show how such a dynamically changing bistable switch can provide a cell with better control over the timing of cell cycle transitions. Moreover, cell cycle oscillations built on bistable switches are more robust when the bistability is modulated in time. Our results are not specific to cell cycle models and may apply to other bistable systems in which the bistable response curve is time-dependent. Many systems in nature show bistability, which means they can evolve to one of two stable steady states under exactly the same conditions. Which state they evolve to depends on where the system comes from. Such bistability underlies the switching behavior that is essential for cells to progress in the cell division cycle. A quick switch happens when the cell jumps from one steady state to another steady state. Typical of this switching behavior is its robustness and irreversibility. In this paper, we expand this viewpoint of the dynamics of the cell cycle by considering bistable switches which themselves are changing in time. This gives the cell an extra layer of control over transitions both in time and in space, and can make those transitions more robust. Such dynamically changing bistability can appear very naturally. We show this in a model of mitotic entry, in which we include a nuclear and cytoplasmic compartment. The activity of a crucial cell cycle protein follows a bistable switch in each compartment, but the shape of its response is changing in time as proteins are imported into and exported from the nucleus.
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Affiliation(s)
- Jan Rombouts
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven (KU Leuven), B-3000 Leuven, Belgium
- * E-mail: (J.R.); (L.G.)
| | - Lendert Gelens
- Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven (KU Leuven), B-3000 Leuven, Belgium
- * E-mail: (J.R.); (L.G.)
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24
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Proskurkin IS, Smelov PS, Vanag VK. Experimental verification of an opto-chemical "neurocomputer". Phys Chem Chem Phys 2020; 22:19359-19367. [PMID: 32822448 DOI: 10.1039/d0cp01858a] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Abstract
A theoretically predicted hierarchical network of pulse coupled chemical micro-oscillators and excitable micro-cells that we call a chemical "neurocomputer" (CN) or even a chemical "brain" is tested experimentally using the Belousov-Zhabotinsky reaction. The CN consists of five functional units: (1) a central pattern generator (CPG), (2) an antenna, (3) a reader for the CPG, (4) a reader for the antenna unit, and (5) a decision making (DM) unit. A hybrid CN, in which such chemical units as readers and DM units are replaced by electronic units, is tested as well. All these variations of the CN respond intelligently to external signals, since they perform an automatic transition from a current to a new dynamic mode of the CPG, which is similar to the antenna dynamic mode that in turn is induced by external signals. In other words, we show for the first time that a network of pulse coupled chemical micro-oscillators is capable of intelligent adaptive behavior.
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Affiliation(s)
- Ivan S Proskurkin
- Centre for Nonlinear Chemistry, Immanuel Kant Baltic Federal University, Kaliningrad, 236041, Russia.
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25
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Halekotte L, Feudel U. Minimal fatal shocks in multistable complex networks. Sci Rep 2020; 10:11783. [PMID: 32678252 PMCID: PMC7366637 DOI: 10.1038/s41598-020-68805-6] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2020] [Accepted: 06/29/2020] [Indexed: 11/15/2022] Open
Abstract
Multistability is a common phenomenon which naturally occurs in complex networks. Often one of the coexisting stable states can be identified as being the desired one for a particular application. We present here a global approach to identify the minimal perturbation which will instantaneously kick the system out of the basin of attraction of its desired state and hence induce a critical or fatal transition we call shock-tipping. The corresponding Minimal Fatal Shock is a vector whose length can be used as a global stability measure and whose direction in state space allows us to draw conclusions on weaknesses of the network corresponding to critical network motifs. We demonstrate this approach in plant-pollinator networks and the power grid of Great Britain. In both system classes, tree-like substructures appear to be the most vulnerable with respect to the minimal shock perturbation.
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Affiliation(s)
- Lukas Halekotte
- Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Carl-von-Ossietzky-Straße 9-11, PO box 2503, 26111, Oldenburg, Germany.
| | - Ulrike Feudel
- Institute for Chemistry and Biology of the Marine Environment, Carl von Ossietzky University Oldenburg, Carl-von-Ossietzky-Straße 9-11, PO box 2503, 26111, Oldenburg, Germany
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26
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Lembo V, Lucarini V, Ragone F. Beyond Forcing Scenarios: Predicting Climate Change through Response Operators in a Coupled General Circulation Model. Sci Rep 2020; 10:8668. [PMID: 32457414 PMCID: PMC7250835 DOI: 10.1038/s41598-020-65297-2] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/02/2020] [Accepted: 04/23/2020] [Indexed: 11/30/2022] Open
Abstract
Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Here we show how to use statistical mechanics to construct operators able to flexibly predict climate change. We perform our study using a fully coupled model - MPI-ESM v.1.2 - and for the first time we prove the effectiveness of response theory in predicting future climate response to CO2 increase on a vast range of temporal scales, from inter-annual to centennial, and for very diverse climatic variables. We investigate within a unified perspective the transient climate response and the equilibrium climate sensitivity, and assess the role of fast and slow processes. The prediction of the ocean heat uptake highlights the very slow relaxation to a newly established steady state. The change in the Atlantic Meridional Overturning Circulation (AMOC) and of the Antarctic Circumpolar Current (ACC) is accurately predicted. The AMOC strength is initially reduced and then undergoes a slow and partial recovery. The ACC strength initially increases due to changes in the wind stress, then undergoes a slowdown, followed by a recovery leading to a overshoot with respect to the initial value. Finally, we are able to predict accurately the temperature change in the North Atlantic.
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Affiliation(s)
- Valerio Lembo
- CEN, Meteorological Institute, Universität Hamburg, Hamburg, Germany
| | - Valerio Lucarini
- CEN, Meteorological Institute, Universität Hamburg, Hamburg, Germany.
- Department of Mathematics and Statistics, University of Reading, Reading, UK.
- Centre for the Mathematics of Planet Earth, University of Reading, Reading, UK.
| | - Francesco Ragone
- Laboratoire de Physique, ENS de Lyon, Université Claude Bernard, Université Lyon, CNRS, Lyon, F-69342, France
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27
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Lan BL, Liew YW, Toda M, Kamsani SH. Flickering of cardiac state before the onset and termination of atrial fibrillation. CHAOS (WOODBURY, N.Y.) 2020; 30:053137. [PMID: 32491883 DOI: 10.1063/1.5130524] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/04/2019] [Accepted: 04/22/2020] [Indexed: 06/11/2023]
Abstract
Complex dynamical systems can shift abruptly from a stable state to an alternative stable state at a tipping point. Before the critical transition, the system either slows down in its recovery rate or flickers between the basins of attraction of the alternative stable states. Whether the heart critically slows down or flickers before it transitions into and out of paroxysmal atrial fibrillation (PAF) is still an open question. To address this issue, we propose a novel definition of cardiac states based on beat-to-beat (RR) interval fluctuations derived from electrocardiogram data. Our results show the cardiac state flickers before PAF onset and termination. Prior to onset, flickering is due to a "tug-of-war" between the sinus node (the natural pacemaker) and atrial ectopic focus/foci (abnormal pacemakers), or the pacing by the latter interspersed among the pacing by the former. It may also be due to an abnormal autonomic modulation of the sinus node. This abnormal modulation may be the sole cause of flickering prior to termination since atrial ectopic beats are absent. Flickering of the cardiac state could potentially be used as part of an early warning or screening system for PAF and guide the development of new methods to prevent or terminate PAF. The method we have developed to define system states and use them to detect flickering can be adapted to study critical transition in other complex systems.
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Affiliation(s)
- Boon Leong Lan
- Electrical and Computer Systems Engineering & Advanced Engineering Platform, School of Engineering, Monash University, 47500 Bandar Sunway, Malaysia
| | - Yew Wai Liew
- Electrical and Computer Systems Engineering & Advanced Engineering Platform, School of Engineering, Monash University, 47500 Bandar Sunway, Malaysia
| | - Mikito Toda
- Laboratory of Non-equilibrium Dynamics, Research Group of Physics, Faculty Division of Natural Sciences, Nara Women's University, Nara 630-8506, Japan
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28
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Maguire OR, Wong ASY, Westerdiep JH, Huck WTS. Early warning signals in chemical reaction networks. Chem Commun (Camb) 2020; 56:3725-3728. [DOI: 10.1039/d0cc01010c] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Many natural and man-made complex systems display early warning signals when close to an abrupt shift in behaviour. Here we show that such early warning signals appear in a complex chemical reaction network.
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Affiliation(s)
- Oliver R. Maguire
- Institute for Molecules and Materials
- Radboud University
- 6525 AJ Nijmegen
- The Netherlands
| | - Albert S. Y. Wong
- Department of Chemistry and Chemical Biology
- Harvard University
- Cambridge
- USA
| | - Jan Harm Westerdiep
- Institute for Molecules and Materials
- Radboud University
- 6525 AJ Nijmegen
- The Netherlands
| | - Wilhelm T. S. Huck
- Institute for Molecules and Materials
- Radboud University
- 6525 AJ Nijmegen
- The Netherlands
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29
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Continuum Modeling of Discrete Plant Communities: Why Does It Work and Why Is It Advantageous? MATHEMATICS 2019. [DOI: 10.3390/math7100987] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Understanding ecosystem response to drier climates calls for modeling the dynamics of dryland plant populations, which are crucial determinants of ecosystem function, as they constitute the basal level of whole food webs. Two modeling approaches are widely used in population dynamics, individual (agent)-based models and continuum partial-differential-equation (PDE) models. The latter are advantageous in lending themselves to powerful methodologies of mathematical analysis, but the question of whether they are suitable to describe small discrete plant populations, as is often found in dryland ecosystems, has remained largely unaddressed. In this paper, we first draw attention to two aspects of plants that distinguish them from most other organisms—high phenotypic plasticity and dispersal of stress-tolerant seeds—and argue in favor of PDE modeling, where the state variables that describe population sizes are not discrete number densities, but rather continuous biomass densities. We then discuss a few examples that demonstrate the utility of PDE models in providing deep insights into landscape-scale behaviors, such as the onset of pattern forming instabilities, multiplicity of stable ecosystem states, regular and irregular, and the possible roles of front instabilities in reversing desertification. We briefly mention a few additional examples, and conclude by outlining the nature of the information we should and should not expect to gain from PDE model studies.
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30
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Wilkat T, Rings T, Lehnertz K. No evidence for critical slowing down prior to human epileptic seizures. CHAOS (WOODBURY, N.Y.) 2019; 29:091104. [PMID: 31575122 DOI: 10.1063/1.5122759] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2019] [Accepted: 08/23/2019] [Indexed: 06/10/2023]
Abstract
There is an ongoing debate whether generic early warning signals for critical transitions exist that can be applied across diverse systems. The human epileptic brain is often considered as a prototypical system, given the devastating and, at times, even life-threatening nature of the extreme event epileptic seizure. More than three decades of international effort has successfully identified predictors of imminent seizures. However, the suitability of typically applied early warning indicators for critical slowing down, namely, variance and lag-1 autocorrelation, for indexing seizure susceptibility is still controversially discussed. Here, we investigated long-term, multichannel recordings of brain dynamics from 28 subjects with epilepsy. Using a surrogate-based evaluation procedure of sensitivity and specificity of time-resolved estimates of early warning indicators, we found no evidence for critical slowing down prior to 105 epileptic seizures.
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Affiliation(s)
- Theresa Wilkat
- Department of Epileptology, University of Bonn Medical Centre, Venusberg-Campus 1, 53127 Bonn, Germany
| | - Thorsten Rings
- Department of Epileptology, University of Bonn Medical Centre, Venusberg-Campus 1, 53127 Bonn, Germany
| | - Klaus Lehnertz
- Department of Epileptology, University of Bonn Medical Centre, Venusberg-Campus 1, 53127 Bonn, Germany
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Proskurkin IS, Smelov PS, Vanag VK. Experimental Investigation of the Dynamical Modes of Four Pulse‐Coupled Chemical Micro‐Oscillators. Chemphyschem 2019; 20:2162-2165. [DOI: 10.1002/cphc.201900421] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2019] [Revised: 07/15/2019] [Indexed: 11/07/2022]
Affiliation(s)
- Ivan S. Proskurkin
- Centre for Nonlinear ChemistryImmanuel Kant Baltic Federal University Kaliningrad 236041 Russia
| | - Pavel S. Smelov
- Centre for Nonlinear ChemistryImmanuel Kant Baltic Federal University Kaliningrad 236041 Russia
| | - Vladimir K. Vanag
- Centre for Nonlinear ChemistryImmanuel Kant Baltic Federal University Kaliningrad 236041 Russia
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32
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Steinbock O, Wackerbauer R, Horváth D. Nonlinear Chemical Dynamics and Its Interdisciplinary Impact: Dedicated to Ken Showalter on the Occasion of his 70th Birthday. CHAOS (WOODBURY, N.Y.) 2019; 29:080401. [PMID: 31472519 DOI: 10.1063/1.5120508] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2019] [Accepted: 07/18/2019] [Indexed: 05/22/2023]
Affiliation(s)
- Oliver Steinbock
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, USA
| | - Renate Wackerbauer
- Department of Physics, University of Alaska, Fairbanks, Alaska 99775-5920, USA
| | - Dezső Horváth
- Department of Applied and Environmental Chemistry, University of Szeged, Rerrich Béla tér 1, Szeged H-6720, Hungary
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33
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Vanag VK. Hierarchical network of pulse coupled chemical oscillators with adaptive behavior: Chemical neurocomputer. CHAOS (WOODBURY, N.Y.) 2019; 29:083104. [PMID: 31472522 DOI: 10.1063/1.5099979] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2019] [Accepted: 06/26/2019] [Indexed: 06/10/2023]
Abstract
We consider theoretically a network of pulse coupled oscillators with time delays. Each oscillator is described by the Oregonator-like model for the Belousov-Zhabotinsky (BZ) reaction. Different groups of oscillators constitute five functional units: (1) a central pattern generator (CPG), (2) a "reader" unit that can identify dynamical modes of the CPG, (3) an antenna (A) unit that receives external signals and responds on them by generating different dynamical modes, (4) another reader unit for identification of the dynamical modes in the A unit, and (5) a decision making unit that switches the current dynamical mode of the CPG to the mode that is similar to the current mode in the A unit. We call this network a chemical neurocomputer, since chemical BZ reaction occurs in each micro-oscillator, while pulse connectivity of these cells is inspired by the brain.
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Affiliation(s)
- Vladimir K Vanag
- Center for Nonlinear Chemistry, Immanuel Kant Baltic Federal University, 14 A. Nevskogo Str., Kaliningrad 236041, Russia
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34
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Kaszás B, Feudel U, Tél T. Tipping phenomena in typical dynamical systems subjected to parameter drift. Sci Rep 2019; 9:8654. [PMID: 31209252 PMCID: PMC6572843 DOI: 10.1038/s41598-019-44863-3] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Accepted: 05/20/2019] [Indexed: 11/08/2022] Open
Abstract
Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics. Based on the example of a paradigmatic low-dimensional dissipative system subjected to different scenarios of parameter drifts of non-negligible rates, we show that a number of novel types of tippings can be observed due to the topological complexity underlying general systems. Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. Tipping from or through an extended chaotic attractor might lead to random tipping into coexisting regular attractors, and rate-induced tippings appear not abruptly as phase transitions, rather they show up gradually when the rate of the parameter drift is increased. Since chaotic systems of arbitrary time-dependence call for ensemble methods, we argue for a probabilistic approach and propose the use of tipping probabilities as a measure of tipping. We numerically determine these quantities and their parameter dependence for all tipping forms discussed.
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Affiliation(s)
- Bálint Kaszás
- Institute for Theoretical Physics, Eötvös Loránd University, Pázmány Péter Sétány 1/A, H-1117, Budapest, Hungary.
| | - Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129, Oldenburg, Germany
| | - Tamás Tél
- Institute for Theoretical Physics, Eötvös Loránd University, Pázmány Péter Sétány 1/A, H-1117, Budapest, Hungary
- MTA-ELTE Theoretical Physics Research Group, Pázmány Péter Sétány 1/A, H-1117, Budapest, Hungary
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35
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Lucarini V, Bódai T. Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View. PHYSICAL REVIEW LETTERS 2019; 122:158701. [PMID: 31050495 DOI: 10.1103/physrevlett.122.158701] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/16/2018] [Indexed: 06/09/2023]
Abstract
The Earth is well known to be, in the current astronomical configuration, in a regime where two asymptotic states can be realized. The warm state we live in is in competition with the ice-covered snowball state. The bistability exists as a result of the positive ice-albedo feedback. In a previous investigation performed on a intermediate complexity climate model we identified the unstable climate states (melancholia states) separating the coexisting climates, and studied their dynamical and geometrical properties. The melancholia states are ice covered up to the midlatitudes and attract trajectories initialized on the basin boundary. In this Letter, we study how stochastically perturbing the parameter controlling the intensity of the incoming solar radiation impacts the stability of the climate. We detect transitions between the warm and the snowball state and analyze in detail the properties of the noise-induced escapes from the corresponding basins of attraction. We determine the most probable paths for the transitions and find evidence that the melancholia states act as gateways, similarly to saddle points in an energy landscape.
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Affiliation(s)
- Valerio Lucarini
- Centre for the Mathematics of Planet Earth, University of Reading, Reading, RG66AX United Kingdom
- Department of Mathematics and Statistics, University of Reading, Reading, RG66AX United Kingdom
- CEN, University of Hamburg, Hamburg, 20144 Germany
| | - Tamás Bódai
- Centre for the Mathematics of Planet Earth, University of Reading, Reading, RG66AX United Kingdom
- Department of Mathematics and Statistics, University of Reading, Reading, RG66AX United Kingdom
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Vanag VK. "Cognitive" modes in small networks of almost identical chemical oscillators with pulsatile inhibitory coupling. CHAOS (WOODBURY, N.Y.) 2019; 29:033106. [PMID: 30927858 DOI: 10.1063/1.5063322] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/26/2018] [Accepted: 02/11/2019] [Indexed: 06/09/2023]
Abstract
The Lavrova-Vanag (LV) model of the periodical Belousov-Zhabotinsky (BZ) reaction has been investigated at pulsed self-perturbations, when a sharp spike of the BZ reaction induces a short inhibitory pulse that perturbs the BZ reaction after some time τ since each spike. The dynamics of this BZ system is strongly dependent on the amplitude Cinh of the perturbing pulses. At Cinh > Ccr, a new pseudo-steady state (SS) emerges far away from the limit cycle of the unperturbed BZ oscillator. The perturbed BZ system spends rather long time in the vicinity of this pseudo-SS, which serves as a trap for phase trajectories. As a result, the dynamics of the BZ system changes qualitatively. We observe new modes with packed spikes separated by either long "silent" dynamics or small-amplitude oscillations around pseudo-SS, depending on Cinh. Networks of two or three LV-BZ oscillators with strong pulsatile coupling and self-inhibition are able to generate so-called "cognitive" modes, which are very sensitive to small changes in Cinh. We demonstrate how the coupling between the BZ oscillators in these networks should be organized to find "cognitive" modes.
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Affiliation(s)
- Vladimir K Vanag
- Centre for Nonlinear Chemistry, Immanuel Kant Baltic Federal University, 14 A. Nevskogo Str., Kaliningrad 236041, Russia
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37
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Smelov PS, Proskurkin IS, Vanag VK. Controllable switching between stable modes in a small network of pulse-coupled chemical oscillators. Phys Chem Chem Phys 2019; 21:3033-3043. [DOI: 10.1039/c8cp07374k] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Switching between stable oscillatory modes in a network of four Belousov–Zhabotinsky oscillators unidirectionally coupled in a ring analysed computationally and experimentally.
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Affiliation(s)
- Pavel S. Smelov
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad
- Russia
| | - Ivan S. Proskurkin
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad
- Russia
| | - Vladimir K. Vanag
- Centre for Nonlinear Chemistry
- Immanuel Kant Baltic Federal University
- Kaliningrad
- Russia
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