An integrative quantifier of multistability in complex systems based on ecological resilience

Mitra, Chiranjit; Kurths, Jürgen; Donner, Reik V.

doi:10.1038/srep16196

Cited by 62 publications

(58 citation statements)

References 28 publications

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“…In order to deepen the understanding of stability in different contexts, e.g., in partial synchronization, more subtle definitions should be considered. Progress in this direction has been made recently [333,334].…”

Section: Correlation With Network Topologymentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

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Synchronization of an ensemble of oscillators is an emergent phenomenon present in several complex systems, ranging from social and physical to biological and technological systems. The most successful approach to describe how coherent behavior emerges in these complex systems is given by the paradigmatic Kuramoto model. This model has been traditionally studied in complete graphs. However, besides being intrinsically dynamical, complex systems present very heterogeneous structure, which can be represented as complex networks. This report is dedicated to review main contributions in the field of synchronization in networks of Kuramoto oscillators. In particular, we provide an overview of the impact of network patterns on the local and global dynamics of coupled phase oscillators. We cover many relevant topics, which encompass a description of the most used analytical approaches and the analysis of several numerical results. Furthermore, we discuss recent developments on variations of the Kuramoto model in networks, including the presence of noise and inertia. The rich potential for applications is discussed for special fields in engineering, neuroscience, physics and Earth science. Finally, we conclude by discussing problems that remain open after the last decade of intensive research on the Kuramoto model and point out some promising directions for future research.

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Section: Correlation With Network Topologymentioning

confidence: 99%

The Kuramoto model in complex networks

et al. 2016

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“…Grimm and Wissel (1997) stressed 346 the large number of definitions that have appeared in Ecology [23]. These definitions 347 are classified into six classes that resume the concepts frequently used in this field: 348 constancy, resilience, persistence, resistance, elasticity, and domain of attraction [24]. In 349 some point or another all of them appear in this work.…”

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confidence: 98%

“…Unfortunately, despite the large number of papers devoted 12 to study the relationship between biodiversity and stability in ecosystems [3,5], there There are several examples where the species ability to modify their environment are 23 specially relevant. Tumor cells are able to modify the surrounding tissues by segregating 24 chemical substances that increase the fitness of malign cells [13]. Soil modification by 25 microbial communities is being reported as one of the main driving factors of these 26 ecosystems [14].…”

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confidence: 99%

Enabling stable coexistence by modifying the environment

Pastor¹,

Nuño

Olarrea³

et al. 2019

Preprint

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AbstractIn this work coexistence is studied using a model based on two classical population models: the quasispecies of Eigen [1] and the daisyworld presented by Watson and Lovelock [2]. It is assumed that species are able to modify the environment. We show that this ability enables the coexistence between, at most, two species in equilibrium. Given an initial population, the problem arises as to determine which of the many equilibrium populations, i.e. extinction, only one species or coexistence of two species, will be reached as a function of the species characteristics, specifically their capacity to modify the environment and the optimal growth rate. These results are obtained under general assumptions, which broadens its applicability to other fields as evolutionary biology and social sciences.

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“…These papers consider small perturbations and put focus on local measures. Mitra et al [20] consider an integrative quantifier of resilience based on both local and nonlocal theory. Their measure builds upon the three aspects of resilience by Walker et al [30]: latitude, resistance and precariousness.…”

Section: Alternative Measures and Topics For Future Researchmentioning

confidence: 99%

“…Mitra et al [20] suggest an integrative measure of resilience based on both local and nonlocal features, and Lundström et al [21] use a simple nonlocal resilience measure for evaluating harvesting strategies of age-and stage-structured populations. However, our impression is that, in analogue with the literature on pure stability measures discussed above, the nonlocal approach is under-used also in the setting of resilience.…”

Section: Introductionmentioning

confidence: 99%

How to find simple nonlocal stability and resilience measures

Lundström

2018

Nonlinear Dyn

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Stability of dynamical systems is a central topic with applications in widespread areas such as economy, biology, physics and mechanical engineering. The dynamics of nonlinear systems may completely change due to perturbations forcing the solution to jump from a safe state into another, possibly dangerous, attractor. Such phenomena cannot be traced by the widespread local stability and resilience measures, based on linearizations, accounting only for arbitrary small perturbations. Using numerical estimates of the size and shape of the basin of attraction, as well as the systems returntime to the attractor after given a perturbation, we construct simple nonlocal stability and resilience measures that record a systems ability to tackle both large and small perturbations. We demonstrate our approach on the Solow-Swan model of economic growth, an electro-mechanical system, a stage-structured population model as well as on a highdimensional system, and conclude that the suggested measures detect dynamic behavior, crucial for a systems stability and resilience, which can be completely missed by local measures. The presented measures are also easy to implement on a standard laptop computer. We believe that our approach will constitute an important step toward filling a current gap in the literature by putting forward and explaining simple ideas and meth-N. L. P. Lundström (B) Department of Mathematics and Mathematical Statistics, Umeå University, 90187 Umeå, Sweden e-mail: niklas.lundstrom@umu.se ods, and by delivering explicit constructions of several promising nonlocal stability and resilience measures.

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An integrative quantifier of multistability in complex systems based on ecological resilience

Cited by 62 publications

References 28 publications

The Kuramoto model in complex networks

The Kuramoto model in complex networks

Enabling stable coexistence by modifying the environment

How to find simple nonlocal stability and resilience measures

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