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Li L, Pang YZ, Sun GQ, Ruan S. Impact of climate change on vegetation patterns in Altay Prefecture, China. MATHEMATICAL MEDICINE AND BIOLOGY : A JOURNAL OF THE IMA 2024; 41:53-80. [PMID: 38421157 DOI: 10.1093/imammb/dqae002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2023] [Revised: 12/18/2023] [Accepted: 02/20/2024] [Indexed: 03/02/2024]
Abstract
Altay Prefecture, a typical arid region in northwestern China, has experienced the climate transition from warming-drying to warming-wetting since 1980s and has attracted widespread attention. Nonetheless, it is still unclear how climate change has influenced the distribution of vegetation in this region. In this paper, a reaction-diffusion model of the climate-vegetation system is proposed to study the impact of climate change (precipitation, temperature and carbon dioxide concentration) on vegetation patterns in Altay Prefecture. Our results indicate that the tendency of vegetation growth in Altay Prefecture improved gradually from 1985 to 2010. Under the current climate conditions, the increase of precipitation results in the change of vegetation pattern structures, and eventually vegetation coverage tends to be uniform. Moreover, we found that there exists an optimal temperature where the spot vegetation pattern structure remains stable. Furthermore, the increase in carbon dioxide concentration induces vegetation pattern transition. Based on four climate change scenarios of the Coupled Model Intercomparison Project Phase 6 (CMIP6), we used the power law range (PLR) to predict the optimal scenario for the sustainable development of the vegetation ecosystem in Altay Prefecture.
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Affiliation(s)
- Li Li
- School of Computer and Information Technology, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Yi-Zhi Pang
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
| | - Gui-Quan Sun
- Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China
- Department of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
| | - Shigui Ruan
- Department of Mathematics, University of Miami, Coral Gables, FL 33146, USA
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2
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Akakpo EK, Haelterman M, Leo F, Parra-Rivas P. Emergence of collapsed snaking related dark and bright Kerr dissipative solitons with quartic-quadratic dispersion. Phys Rev E 2023; 108:014203. [PMID: 37583153 DOI: 10.1103/physreve.108.014203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2023] [Accepted: 05/23/2023] [Indexed: 08/17/2023]
Abstract
We theoretically investigate the dynamics, bifurcation structure, and stability of dark localized states emerging in Kerr cavities in the presence of positive second- and fourth-order dispersion. In this previously unexplored regime, dark states form through the locking of uniform wave fronts, or domain walls, connecting two coexisting stable uniform states, and undergo a generic bifurcation structure known as collapsed homoclinic snaking. We characterize the robustness of these states by computing their stability and bifurcation structure as a function of the main control parameter of the system. Furthermore, we show that by increasing the dispersion of fourth order, bright localized states can be also stabilized.
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Affiliation(s)
- Edem Kossi Akakpo
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Marc Haelterman
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Francois Leo
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
| | - Pedro Parra-Rivas
- OPERA-photonics, Université libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium
- Dipartimento di Ingegneria dell'Informazione, Elettronica e Telecomunicazioni, Sapienza Universitá di Roma, via Eudossiana 18, 00184 Rome, Italy
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3
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Al Saadi F, Parra-Rivas P. Transitions between dissipative localized structures in the simplified Gilad-Meron model for dryland plant ecology. CHAOS (WOODBURY, N.Y.) 2023; 33:033129. [PMID: 37003806 DOI: 10.1063/5.0133576] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2022] [Accepted: 02/15/2023] [Indexed: 06/19/2023]
Abstract
Spatially extended patterns and multistability of possible different states are common in many ecosystems, and their combination has an important impact on their dynamical behaviors. One potential combination involves tristability between a patterned state and two different uniform states. Using a simplified version of the Gilad-Meron model for dryland ecosystems, we study the organization, in bifurcation terms, of the localized structures arising in tristable regimes. These states are generally related to the concept of wave front locking and appear in the form of spots and gaps of vegetation. We find that the coexistence of localized spots and gaps, within tristable configurations, yields the appearance of hybrid states. We also study the emergence of spatiotemporal localized states consisting of a portion of a periodic pattern embedded in a uniform Hopf-like oscillatory background in a subcritical Turing-Hopf dynamical regime.
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Affiliation(s)
- Fahad Al Saadi
- Department of Systems Engineering, Military Technological College, Muscat, Oman
| | - Pedro Parra-Rivas
- Dipartimento di Ingegneria dell'Informazione, Elettronica e Telecomunicazioni, Sapienza Universitá di Roma, via Eudossiana 18, 00184 Rome, Italy
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4
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Consolo G, Curró C, Grifó G, Valenti G. Oscillatory periodic pattern dynamics in hyperbolic reaction-advection-diffusion models. Phys Rev E 2022; 105:034206. [PMID: 35428106 DOI: 10.1103/physreve.105.034206] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2021] [Accepted: 01/24/2022] [Indexed: 11/07/2022]
Abstract
In this work we consider a quite general class of two-species hyperbolic reaction-advection-diffusion system with the main aim of elucidating the role played by inertial effects in the dynamics of oscillatory periodic patterns. To this aim, first, we use linear stability analysis techniques to deduce the conditions under which wave (or oscillatory Turing) instability takes place. Then, we apply multiple-scale weakly nonlinear analysis to determine the equation which rules the spatiotemporal evolution of pattern amplitude close to criticality. This investigation leads to a cubic complex Ginzburg-Landau (CCGL) equation which, owing to the functional dependence of the coefficients here involved on the inertial times, reveals some intriguing consequences. To show in detail the richness of such a scenario, we present, as an illustrative example, the pattern dynamics occurring in the hyperbolic generalization of the extended Klausmeier model. This is a simple two-species model used to describe the migration of vegetation stripes along the hillslope of semiarid environments. By means of a thorough comparison between analytical predictions and numerical simulations, we show that inertia, apart from enlarging the region of the parameter plane where wave instability occurs, may also modulate the key features of the coherent structures, solution of the CCGL equation. In particular, it is proven that inertial effects play a role, not only during transient regime from the spatially-homogeneous steady state toward the patterned state, but also in altering the amplitude, the wavelength, the angular frequency, and even the stability of the phase-winding solutions.
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Affiliation(s)
- Giancarlo Consolo
- Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy
| | - Carmela Curró
- Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy
| | - Gabriele Grifó
- Department of Mathematical, Computer, Physical and Earth Sciences, University of Messina (Italy) V.le F. Stagno D'Alcontres 31, I-98166 Messina, Italy
| | - Giovanna Valenti
- Department of Engineering, University of Messina (Italy) C.da di Dio, I-98166 Messina, Italy
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5
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Belowground feedbacks as drivers of spatial self-organization and community assembly. Phys Life Rev 2021; 38:1-24. [PMID: 34334324 DOI: 10.1016/j.plrev.2021.07.002] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Accepted: 07/12/2021] [Indexed: 02/03/2023]
Abstract
Vegetation patterning in water-limited and other resource-limited ecosystems highlights spatial self-organization processes as potentially key drivers of community assembly. These processes provide insight into predictable landscape-level relationships between organisms and their abiotic environment in the form of regular and irregular patterns of biota and resources. However, two aspects have largely been overlooked; the roles played by plant - soil-biota feedbacks and allelopathy in spatial self-organization, and their potential contribution, along with plant-resource feedbacks, to community assembly through spatial self-organization. Here, we expand the drivers of spatial self-organization from a focus on plant-resource feedbacks to include plant - soil-biota feedbacks and allelopathy, and integrate concepts of nonlinear physics and community ecology to generate a new hypothesis. According to this hypothesis, below-ground processes can affect community assemblages through two types of spatial self-organization, global and local. The former occurs simultaneously across whole ecosystems, leading to self-organized patterns of biota, allelochemicals and resources, and niche partitioning. The latter occurs locally in ecotones, and determines ecotone structure and motion, invasion dynamics, and species coexistence. Studies of the two forms of spatial self-organization are important for understanding the organization of plant communities in drier climates which are likely to involve spatial patterning or re-patterning. Such studies are also important for developing new practices of ecosystem management, based on local manipulations at ecotones, to slow invasion dynamics or induce transitions from transitive to intransitive networks of interspecific interactions which increase species diversity.
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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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7
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Cisternas J, Rohe K, Wehner S. Reaction-diffusion fronts and the butterfly set. CHAOS (WOODBURY, N.Y.) 2020; 30:113138. [PMID: 33261332 DOI: 10.1063/5.0022298] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2020] [Accepted: 11/02/2020] [Indexed: 06/12/2023]
Abstract
A single-species reaction-diffusion model is used for studying the coexistence of multiple stable steady states. In these systems, one can define a potential-like functional that contains the stability properties of the states, and the essentials of the motion of wave fronts in one- and two-dimensional space. Using a quintic polynomial for the reaction term and taking advantage of the well-known butterfly bifurcation, we analyze the different scenarios involving the competition of two and three stable steady states, based on equipotential curves and points in parameter space. The predicted behaviors, including a front splitting instability, are contrasted to numerical integrations of reaction fronts in two dimensions.
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Affiliation(s)
- Jaime Cisternas
- Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Chile, Monse nor Alvaro del Portillo 12455, Santiago 7620001, Chile
| | - Kevin Rohe
- Surface Science Group, Institute for Integrated Natural Sciences, University of Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany
| | - Stefan Wehner
- Surface Science Group, Institute for Integrated Natural Sciences, University of Koblenz-Landau, Universitätsstraße 1, 56070 Koblenz, Germany
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8
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Mas Arabí C, Parra-Rivas P, Hansson T, Gelens L, Wabnitz S, Leo F. Localized structures formed through domain wall locking in cavity-enhanced second-harmonic generation. OPTICS LETTERS 2020; 45:5856-5859. [PMID: 33057302 DOI: 10.1364/ol.399658] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2020] [Accepted: 09/22/2020] [Indexed: 06/11/2023]
Abstract
We analyze the formation of localized structures in cavity-enhanced second-harmonic generation. We focus on the phase-matched limit, and consider that fundamental and generated waves have opposite signs of group velocity dispersion. We show that these states form due to the locking of domain walls connecting two stable homogeneous states of the system, and undergo collapsed snaking. We study the impact of temporal walk-off on the stability and dynamics of these localized states.
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9
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Eigentler L, Sherratt JA. An integrodifference model for vegetation patterns in semi-arid environments with seasonality. J Math Biol 2020; 81:875-904. [PMID: 32888058 PMCID: PMC7519009 DOI: 10.1007/s00285-020-01530-w] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Revised: 03/04/2020] [Indexed: 11/26/2022]
Abstract
Vegetation patterns are a characteristic feature of semi-deserts occurring on all continents except Antarctica. In some semi-arid regions, the climate is characterised by seasonality, which yields a synchronisation of seed dispersal with the dry season or the beginning of the wet season. We reformulate the Klausmeier model, a reaction–advection–diffusion system that describes the plant–water dynamics in semi-arid environments, as an integrodifference model to account for the temporal separation of plant growth processes during the wet season and seed dispersal processes during the dry season. The model further accounts for nonlocal processes involved in the dispersal of seeds. Our analysis focusses on the onset of spatial patterns. The Klausmeier partial differential equations (PDE) model is linked to the integrodifference model in an appropriate limit, which yields a control parameter for the temporal separation of seed dispersal events. We find that the conditions for pattern onset in the integrodifference model are equivalent to those for the continuous PDE model and hence independent of the time between seed dispersal events. We thus conclude that in the context of seed dispersal, a PDE model provides a sufficiently accurate description, even if the environment is seasonal. This emphasises the validity of results that have previously been obtained for the PDE model. Further, we numerically investigate the effects of changes to seed dispersal behaviour on the onset of patterns. We find that long-range seed dispersal inhibits the formation of spatial patterns and that the seed dispersal kernel’s decay at infinity is a significant regulator of patterning.
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Affiliation(s)
- Lukas Eigentler
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh, EH14 4AS UK
- Division of Molecular Microbiology, School of Life Sciences, University of Dundee, Dundee, DD1 5EH UK
- Division of Mathematics, School of Science and Engineering, University of Dundee, Dundee, DD1 4HN UK
| | - Jonathan A. Sherratt
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot Watt University, Edinburgh, EH14 4AS UK
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10
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Parra-Rivas P, Fernandez-Oto C. Formation of localized states in dryland vegetation: Bifurcation structure and stability. Phys Rev E 2020; 101:052214. [PMID: 32575306 DOI: 10.1103/physreve.101.052214] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2019] [Accepted: 04/27/2020] [Indexed: 11/07/2022]
Abstract
We study theoretically the emergence of localized states of vegetation close to the onset of desertification. These states are formed through the locking of vegetation fronts, connecting a uniform vegetation state with a bare soil state, which occurs nearby the Maxwell point of the system. To study these structures we consider a universal model of vegetation dynamics in drylands, which has been obtained as the normal form for different vegetation models. Close to the Maxwell point localized gaps and spots of vegetation exist and undergo collapsed snaking. The presence of gaps strongly suggest that the ecosystem may undergo a recovering process. In contrast, the presence of spots may indicate that the ecosystem is close to desertification.
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Affiliation(s)
- P Parra-Rivas
- Service OPERA-photonics, Universit libre de Bruxelles, 50 Avenue F. D. Roosevelt, CP 194/5, B-1050 Bruxelles, Belgium.,Laboratory of Dynamics in Biological Systems, Department of Cellular and Molecular Medicine, University of Leuven, B-3000 Leuven, Belgium
| | - C Fernandez-Oto
- Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo 12455 Santiago, Chile
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11
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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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12
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Consolo G, Valenti G. Secondary seed dispersal in the Klausmeier model of vegetation for sloped semi-arid environments. Ecol Modell 2019. [DOI: 10.1016/j.ecolmodel.2019.02.009] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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13
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Eigentler L, Sherratt JA. Metastability as a Coexistence Mechanism in a Model for Dryland Vegetation Patterns. Bull Math Biol 2019; 81:2290-2322. [PMID: 31012031 DOI: 10.1007/s11538-019-00606-z] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2018] [Accepted: 04/11/2019] [Indexed: 11/25/2022]
Abstract
Vegetation patterns are a ubiquitous feature of water-deprived ecosystems. Despite the competition for the same limiting resource, coexistence of several plant species is commonly observed. We propose a two-species reaction-diffusion model based on the single-species Klausmeier model, to analytically investigate the existence of states in which both species coexist. Ecologically, the study finds that coexistence is supported if there is a small difference in the plant species' average fitness, measured by the ratio of a species' capabilities to convert water into new biomass to its mortality rate. Mathematically, coexistence is not a stable solution of the system, but both spatially uniform and patterned coexistence states occur as metastable states. In this context, a metastable solution in which both species coexist corresponds to a long transient (exceeding [Formula: see text] years in dimensional parameters) to a stable one-species state. This behaviour is characterised by the small size of a positive eigenvalue which has the same order of magnitude as the average fitness difference between the two species. Two mechanisms causing the occurrence of metastable solutions are established: a spatially uniform unstable equilibrium and a stable one-species pattern which is unstable to the introduction of a competitor. We further discuss effects of asymmetric interspecific competition (e.g. shading) on the metastability property.
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Affiliation(s)
- Lukas Eigentler
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK.
| | - Jonathan A Sherratt
- Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
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14
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Fernandez-Oto C, Tzuk O, Meron E. Front Instabilities Can Reverse Desertification. PHYSICAL REVIEW LETTERS 2019; 122:048101. [PMID: 30768298 DOI: 10.1103/physrevlett.122.048101] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/09/2018] [Revised: 11/26/2018] [Indexed: 06/09/2023]
Abstract
Degradation processes in living systems often take place gradually by front propagation. An important context of such processes is loss of biological productivity in drylands or desertification. Using a dryland-vegetation model, we analyze the stability and dynamics of desertification fronts, identify linear and nonlinear front instabilities, and highlight the significance of these instabilities in inducing self-recovery. The results are based on the derivation and analysis of a universal amplitude equation for pattern-forming living systems for which nonuniform instabilities cannot emerge from the nonviable (zero) state. The results may therefore be applicable to other contexts of animate matter where degradation processes occur by front propagation.
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Affiliation(s)
- Cristian Fernandez-Oto
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Israel
- Complex Systems Group, Facultad de Ingenieria y Ciencias Aplicadas, Universidad de los Andes, Av. Mon. Alvaro del Portillo 12.455 Santiago, Chile
| | - Omer Tzuk
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - Ehud Meron
- Department of Solar Energy and Environmental Physics, BIDR, Ben-Gurion University of the Negev, Sede Boqer Campus, 84990 Israel
- Physics Department, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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15
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Siero E, Siteur K, Doelman A, Koppel JVD, Rietkerk M, Eppinga MB. Grazing Away the Resilience of Patterned Ecosystems. Am Nat 2019; 193:472-480. [PMID: 30794443 DOI: 10.1086/701669] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Abstract
Ecosystems' responses to changing environmental conditions can be modulated by spatial self-organization. A prominent example of this can be found in drylands, where formation of vegetation patterns attenuates the magnitude of degradation events in response to decreasing rainfall. In model studies, the pattern wavelength responds to changing conditions, which is reflected by a rather gradual decline in biomass in response to decreasing rainfall. Although these models are spatially explicit, they have adopted a mean-field approach to grazing. By taking into account spatial variability when modeling grazing, we find that (over)grazing can lead to a dramatic shift in biomass, so that degradation occurs at rainfall rates that would otherwise still maintain a relatively productive ecosystem. Moreover, grazing increases the resilience of degraded ecosystem states. Consequently, restoration of degraded ecosystems could benefit from the introduction of temporary small-scale exclosures to escape from the basin of attraction of degraded states.
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16
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Gandhi P, Zelnik YR, Knobloch E. Spatially localized structures in the Gray-Scott model. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2018; 376:20170375. [PMID: 30420543 PMCID: PMC6232600 DOI: 10.1098/rsta.2017.0375] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 08/21/2018] [Indexed: 05/19/2023]
Abstract
Spatially localized structures in the one-dimensional Gray-Scott reaction-diffusion model are studied using a combination of numerical continuation techniques and weakly nonlinear theory, focusing on the regime in which the activator and substrate diffusivities are different but comparable. Localized states arise in three different ways: in a subcritical Turing instability present in this regime, and from folds in the branch of spatially periodic Turing states. They also arise from the fold of spatially uniform states. These three solution branches interconnect in complex ways. We use numerical continuation techniques to explore their global behaviour within a formulation of the model that has been used to describe dryland vegetation patterns on a flat terrain.This article is part of the theme issue 'Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 2)'.
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Affiliation(s)
- Punit Gandhi
- Mathematical Biosciences Institute, Ohio State University, Columbus, OH 43210, USA
| | - Yuval R Zelnik
- Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, 09200 Moulis, France
| | - Edgar Knobloch
- Department of Physics, University of California, Berkeley, CA 94720, USA
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17
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Feudel U, Pisarchik AN, Showalter K. Multistability and tipping: From mathematics and physics to climate and brain-Minireview and preface to the focus issue. CHAOS (WOODBURY, N.Y.) 2018; 28:033501. [PMID: 29604626 DOI: 10.1063/1.5027718] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Multistability refers to the coexistence of different stable states in nonlinear dynamical systems. This phenomenon has been observed in laboratory experiments and in nature. In this introduction, we briefly introduce the classes of dynamical systems in which this phenomenon has been found and discuss the extension to new system classes. Furthermore, we introduce the concept of critical transitions and discuss approaches to distinguish them according to their characteristics. Finally, we present some specific applications in physics, neuroscience, biology, ecology, and climate science.
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Affiliation(s)
- Ulrike Feudel
- Theoretical Physics/Complex Systems, ICBM, University of Oldenburg, 26129 Oldenburg, Germany
| | - Alexander N Pisarchik
- Center for Biomedical Technology, Technical University of Madrid, Campus Montegancedo, 28223 Pozuelo de Alarcon, Madrid, Spain
| | - Kenneth Showalter
- C. Eugene Bennett Department of Chemistry, West Virginia University, Morgantown, West Virginia 26506-6045, USA
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