1
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van de Leemput IA, Bascompte J, Buddendorf WB, Dakos V, Lever JJ, Scheffer M, van Nes EH. Transformation starts at the periphery of networks where pushback is less. Sci Rep 2024; 14:11344. [PMID: 38762633 PMCID: PMC11102466 DOI: 10.1038/s41598-024-61057-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 04/30/2024] [Indexed: 05/20/2024] Open
Abstract
Complex systems ranging from societies to ecological communities and power grids may be viewed as networks of connected elements. Such systems can go through critical transitions driven by an avalanche of contagious change. Here we ask, where in a complex network such a systemic shift is most likely to start. Intuitively, a central node seems the most likely source of such change. Indeed, topological studies suggest that central nodes can be the Achilles heel for attacks. We argue that the opposite is true for the class of networks in which all nodes tend to follow the state of their neighbors, a category we call two-way pull networks. In this case, a well-connected central node is an unlikely starting point of a systemic shift due to the buffering effect of connected neighbors. As a result, change is most likely to cascade through the network if it spreads first among relatively poorly connected nodes in the periphery. The probability of such initial spread is highest when the perturbation starts from intermediately connected nodes at the periphery, or more specifically, nodes with intermediate degree and relatively low closeness centrality. Our finding is consistent with empirical observations on social innovation, and may be relevant to topics as different as the sources of originality of art, collapse of financial and ecological networks and the onset of psychiatric disorders.
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Affiliation(s)
- Ingrid A van de Leemput
- Department of Environmental Sciences, Wageningen University and Research, Wageningen, The Netherlands.
| | - Jordi Bascompte
- Department of Evolutionary Biology and Environmental Studies, University of Zurich, Zurich, Switzerland
| | | | - Vasilis Dakos
- Institute Des Sciences de L'Évolution, Université de Montpellier, CNRS, IRD, EPHE, Montpellier, France
| | - J Jelle Lever
- Swiss Federal Institute for Forest, Snow and Landscape Research (WSL), Birmensdorf, Switzerland
| | - Marten Scheffer
- Department of Environmental Sciences, Wageningen University and Research, Wageningen, The Netherlands
| | - Egbert H van Nes
- Department of Environmental Sciences, Wageningen University and Research, Wageningen, The Netherlands
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2
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Ishii H, Kori H. Diffusive coupling facilitates and impedes noise-induced escape in interacting bistable elements. Sci Rep 2024; 14:11019. [PMID: 38744886 PMCID: PMC11094171 DOI: 10.1038/s41598-024-61058-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2024] [Accepted: 04/30/2024] [Indexed: 05/16/2024] Open
Abstract
Diverse complex systems often undergo sudden changes in their states, such as epileptic seizures, climate changes, and social uprisings. Such behavior has been modeled by noise-induced escape of bistable elements, which is the escape from an attracting state driven by a fluctuation in the system's state. We consider a system of interacting bistable elements and investigate the effect of diffusive coupling among elements on the process of noise-induced escape. We focus on the influence of the coupling strength over the escape time, which is the time it takes for noise-induced escape to occur. We performed numerical simulations and observed that weak coupling reduced the mean escape time, whereas strong coupling impeded escape. We argue that, although diffusive coupling both facilitates and impedes escape, the facilitating effect is dominant when coupling is weak. For weak coupling cases, we develop an approximate theory that can predict the mean and variance of escape times. In contrast, strong coupling reduces the effective noise intensity to impede escape. Our results suggest that diffusive coupling among multistable elements contributes to regulating the rate of transitions among attracting states.
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Affiliation(s)
- Hidemasa Ishii
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, 277-8561, Japan.
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, 277-8561, Japan
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3
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Staal A, Theeuwen JJE, Wang-Erlandsson L, Wunderling N, Dekker SC. Targeted rainfall enhancement as an objective of forestation. GLOBAL CHANGE BIOLOGY 2024; 30:e17096. [PMID: 38273477 DOI: 10.1111/gcb.17096] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2023] [Revised: 11/15/2023] [Accepted: 11/29/2023] [Indexed: 01/27/2024]
Abstract
Forestation efforts are accelerating across the globe in the fight against global climate change, in order to restore biodiversity, and to improve local livelihoods. Yet, so far the non-local effects of forestation on rainfall have largely remained a blind spot. Here we build upon emerging work to propose that targeted rainfall enhancement may also be considered in the prioritization of forestation. We show that the tools to achieve this are rapidly becoming available, but we also identify drawbacks and discuss which further developments are still needed to realize robust assessments of the rainfall effects of forestation in the face of climate change. Forestation programs may then mitigate not only global climate change itself but also its adverse effects in the form of drying.
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Affiliation(s)
- Arie Staal
- Copernicus Institute of Sustainable Development, Utrecht University, Utrecht, The Netherlands
| | - Jolanda J E Theeuwen
- Copernicus Institute of Sustainable Development, Utrecht University, Utrecht, The Netherlands
- Wetsus, European Centre of Excellence for Sustainable Water Technology, Leeuwarden, The Netherlands
| | - Lan Wang-Erlandsson
- Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden
- Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Potsdam, Germany
- Bolin Centre for Climate Research, Stockholm University, Stockholm, Sweden
| | - Nico Wunderling
- Stockholm Resilience Centre, Stockholm University, Stockholm, Sweden
- Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Potsdam, Germany
- High Meadows Environmental Institute, Princeton University, Princeton, New Jersey, USA
| | - Stefan C Dekker
- Copernicus Institute of Sustainable Development, Utrecht University, Utrecht, The Netherlands
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4
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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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5
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Alkhayuon H, Marley J, Wieczorek S, Tyson RC. Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase-tipping. GLOBAL CHANGE BIOLOGY 2023; 29:3347-3363. [PMID: 37021593 DOI: 10.1111/gcb.16679] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Revised: 02/24/2023] [Accepted: 03/02/2023] [Indexed: 05/16/2023]
Abstract
Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent work indicates that the changing variability, that is, the amplitude and the temporal autocorrelation of deviations from the mean, may have greater and more imminent impact on ecosystems. In this paper, we demonstrate that changes in climate variability alone could drive cyclic predator-prey ecosystems to extinction via so-called phase-tipping (P-tipping), a new type of instability that occurs only from certain phases of the predator-prey cycle. We construct a mathematical model of a variable climate and couple it to two self-oscillating paradigmatic predator-prey models. Most importantly, we combine realistic parameter values for the Canada lynx and snowshoe hare with actual climate data from the boreal forest. In this way, we demonstrate that critically important species in the boreal forest have increased likelihood of P-tipping to extinction under predicted changes in climate variability, and are most vulnerable during stages of the cycle when the predator population is near its maximum. Furthermore, our analysis reveals that stochastic resonance is the underlying mechanism for the increased likelihood of P-tipping to extinction.
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Affiliation(s)
- Hassan Alkhayuon
- School of Mathematical Sciences, University College Cork, Western Road, Cork, T12 XF62, Ireland
| | - Jessa Marley
- CMPS Department (Mathematics), University of British Columbia Okanagan, Kelowna, British Columbia, Canada
| | - Sebastian Wieczorek
- School of Mathematical Sciences, University College Cork, Western Road, Cork, T12 XF62, Ireland
| | - Rebecca C Tyson
- CMPS Department (Mathematics), University of British Columbia Okanagan, Kelowna, British Columbia, Canada
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6
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Ashwin P, Creaser J, Tsaneva-Atanasova K. Quasipotentials for coupled escape problems and the gate-height bifurcation. Phys Rev E 2023; 107:014213. [PMID: 36797857 DOI: 10.1103/physreve.107.014213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.
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Affiliation(s)
- Peter Ashwin
- Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Jennifer Creaser
- Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Krasimira Tsaneva-Atanasova
- Department of Mathematics and Statistics, and EPSRC Hub for Quantitative Modelling in Healthcare, University of Exeter, Exeter EX4 4QJ, United Kingdom and Institute for Advanced Study, Technical University of Munich, Lichtenbergstrasse 2 a, D-85748 Garching, Germany
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7
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Network motifs shape distinct functioning of Earth's moisture recycling hubs. Nat Commun 2022; 13:6574. [PMID: 36323658 PMCID: PMC9630528 DOI: 10.1038/s41467-022-34229-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 10/12/2022] [Indexed: 11/06/2022] Open
Abstract
Earth's hydrological cycle critically depends on the atmospheric moisture flows connecting evaporation to precipitation. Here we convert a decade of reanalysis-based moisture simulations into a high-resolution global directed network of spatial moisture provisions. We reveal global and local network structures that offer a new view of the global hydrological cycle. We identify four terrestrial moisture recycling hubs: the Amazon Basin, the Congo Rainforest, South Asia and the Indonesian Archipelago. Network motifs reveal contrasting functioning of these regions, where the Amazon strongly relies on directed connections (feed-forward loops) for moisture redistribution and the other hubs on reciprocal moisture connections (zero loops and neighboring loops). We conclude that Earth's moisture recycling hubs are characterized by specific topologies shaping heterogeneous effects of land-use changes and climatic warming on precipitation patterns.
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8
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Recurrent droughts increase risk of cascading tipping events by outpacing adaptive capacities in the Amazon rainforest. Proc Natl Acad Sci U S A 2022; 119:e2120777119. [PMID: 35917341 PMCID: PMC9371734 DOI: 10.1073/pnas.2120777119] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
Tipping elements are nonlinear subsystems of the Earth system that have the potential to abruptly shift to another state if environmental change occurs close to a critical threshold with large consequences for human societies and ecosystems. Among these tipping elements may be the Amazon rainforest, which has been undergoing intensive anthropogenic activities and increasingly frequent droughts. Here, we assess how extreme deviations from climatological rainfall regimes may cause local forest collapse that cascades through the coupled forest-climate system. We develop a conceptual dynamic network model to isolate and uncover the role of atmospheric moisture recycling in such tipping cascades. We account for heterogeneity in critical thresholds of the forest caused by adaptation to local climatic conditions. Our results reveal that, despite this adaptation, a future climate characterized by permanent drought conditions could trigger a transition to an open canopy state particularly in the southern Amazon. The loss of atmospheric moisture recycling contributes to one-third of the tipping events. Thus, by exceeding local thresholds in forest adaptive capacity, local climate change impacts may propagate to other regions of the Amazon basin, causing a risk of forest shifts even in regions where critical thresholds have not been crossed locally.
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9
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Kundu P, MacLaren NG, Kori H, Masuda N. Mean-field theory for double-well systems on degree-heterogeneous networks. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0350] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Many complex dynamical systems in the real world, including ecological, climate, financial and power-grid systems, often show critical transitions, or tipping points, in which the system’s dynamics suddenly transit into a qualitatively different state. In mathematical models, tipping points happen as a control parameter gradually changes and crosses a certain threshold. Tipping elements in such systems may interact with each other as a network, and understanding the behaviour of interacting tipping elements is a challenge because of the high dimensionality originating from the network. Here, we develop a degree-based mean-field theory for a prototypical double-well system coupled on a network with the aim of understanding coupled tipping dynamics with a low-dimensional description. The method approximates both the onset of the tipping point and the position of equilibria with a reasonable accuracy. Based on the developed theory and numerical simulations, we also provide evidence for multistage tipping point transitions in networks of double-well systems.
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Affiliation(s)
- Prosenjit Kundu
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
| | - Neil G. MacLaren
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, The University of Tokyo, Chiba 277-8561, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, NY 14260-2900, USA
- Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, NY 14260-5030, USA
- Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
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10
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Kundu P, Kori H, Masuda N. Accuracy of a one-dimensional reduction of dynamical systems on networks. Phys Rev E 2022; 105:024305. [PMID: 35291116 DOI: 10.1103/physreve.105.024305] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2021] [Accepted: 01/20/2022] [Indexed: 06/14/2023]
Abstract
Resilience is an ability of a system with which the system can adjust its activity to maintain its functionality when it is perturbed. To study resilience of dynamics on networks, Gao et al. [Nature (London) 530, 307 (2016)0028-083610.1038/nature16948] proposed a theoretical framework to reduce dynamical systems on networks, which are high dimensional in general, to one-dimensional dynamical systems. The accuracy of this one-dimensional reduction relies on three approximations in addition to the assumption that the network has a negligible degree correlation. In the present study, we analyze the accuracy of the one-dimensional reduction assuming networks without degree correlation. We do so mainly through examining the validity of the individual assumptions underlying the method. Across five dynamical system models, we find that the accuracy of the one-dimensional reduction hinges on the spread of the equilibrium value of the state variable across the nodes in most cases. Specifically, the one-dimensional reduction tends to be accurate when the dispersion of the node's state is small. We also find that the correlation between the node's state and the node's degree, which is common for various dynamical systems on networks, is unrelated to the accuracy of the one-dimensional reduction.
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Affiliation(s)
- Prosenjit Kundu
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260-2900, USA
| | - Hiroshi Kori
- Department of Complexity Science and Engineering, The University of Tokyo, Chiba 277-8561, Japan
| | - Naoki Masuda
- Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260-2900, USA
- Computational and Data-Enabled Science and Engineering Program, State University of New York at Buffalo, Buffalo, New York 14260-5030, USA
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11
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Sun Y, Meng J, Yao Q, Saberi AA, Chen X, Fan J, Kurths J. Percolation analysis of the atmospheric structure. Phys Rev E 2021; 104:064139. [PMID: 35030827 DOI: 10.1103/physreve.104.064139] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 12/10/2021] [Indexed: 06/14/2023]
Abstract
The atmosphere is a thermo-hydrodynamical complex system and provides oxygen to most animal life at the Earth's surface. However, the detection of complexity for the atmosphere remains elusive and debated. Here we develop a percolation-based framework to explore its structure by using the global air temperature field. We find that the percolation threshold is much delayed compared with the prototypical percolation model and the giant cluster eventually emerges explosively. A finite-size-scaling analysis reveals that the observed transition in each atmosphere layer is genuine discontinuous. Furthermore, at the percolation threshold, we uncover that the boundary of the giant cluster is self-affine, with fractal dimension d_{f}, and can be utilized to quantify the atmospheric complexity. Specifically, our results indicate that the complexity of the atmosphere decreases superlinearly with height, i.e., the complexity is higher at the surface than at the top layer and vice versa, due to the atmospheric boundary forcings. The proposed methodology may evaluate and improve our understanding regarding the critical phenomena of the complex Earth system and can be used as a benchmark tool to test the performance of Earth system models.
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Affiliation(s)
- Yu Sun
- School of Systems Science, Beijing Normal University, 100875 Beijing, China
| | - Jun Meng
- School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
- Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
| | - Qing Yao
- School of Systems Science, Beijing Normal University, 100875 Beijing, China
| | - Abbas Ali Saberi
- Department of Physics, University of Tehran, Tehran 14395-547, Iran
- Institut für Theoretische Physik, Universitat zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany
| | - Xiaosong Chen
- School of Systems Science, Beijing Normal University, 100875 Beijing, China
| | - Jingfang Fan
- School of Systems Science, Beijing Normal University, 100875 Beijing, China
- Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, 14412 Potsdam, Germany
- Department of Physics, Humboldt University, 10099 Berlin, Germany
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12
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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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13
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Klose AK, Karle V, Winkelmann R, Donges JF. Emergence of cascading dynamics in interacting tipping elements of ecology and climate. ROYAL SOCIETY OPEN SCIENCE 2020; 7:200599. [PMID: 32742700 PMCID: PMC7353982 DOI: 10.1098/rsos.200599] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2020] [Accepted: 05/18/2020] [Indexed: 05/08/2023]
Abstract
In ecology, climate and other fields, (sub)systems have been identified that can transition into a qualitatively different state when a critical threshold or tipping point in a driving process is crossed. An understanding of those tipping elements is of great interest given the increasing influence of humans on the biophysical Earth system. Complex interactions exist between tipping elements, e.g. physical mechanisms connect subsystems of the climate system. Based on earlier work on such coupled nonlinear systems, we systematically assessed the qualitative long-term behaviour of interacting tipping elements. We developed an understanding of the consequences of interactions on the tipping behaviour allowing for tipping cascades to emerge under certain conditions. The (narrative) application of these qualitative results to real-world examples of interacting tipping elements indicates that tipping cascades with profound consequences may occur: the interacting Greenland ice sheet and thermohaline ocean circulation might tip before the tipping points of the isolated subsystems are crossed. The eutrophication of the first lake in a lake chain might propagate through the following lakes without a crossing of their individual critical nutrient input levels. The possibility of emerging cascading tipping dynamics calls for the development of a unified theory of interacting tipping elements and the quantitative analysis of interacting real-world tipping elements.
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Affiliation(s)
- Ann Kristin Klose
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany
- Carl von Ossietzky University Oldenburg, Oldenburg, Germany
| | - Volker Karle
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany
- Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria
| | - Ricarda Winkelmann
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany
- Department of Physics and Astronomy, University of Potsdam, 14469 Potsdam, Germany
| | - Jonathan F. Donges
- Earth System Analysis, Potsdam Institute for Climate Impact Research, Member of the Leibniz Association, Telegrafenberg A31, 14473 Potsdam, Germany
- Stockholm Resilience Centre, Stockholm University, 10691 Stockholm, Sweden
- Author for correspondence: Jonathan F. Donges e-mail:
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