Linear stability theory as an early warning sign for transitions in high dimensional complex systems

Piovani, Duccio; Grujić, Jelena

doi:10.1088/1751-8113/49/29/295102

Cited by 11 publications

(16 citation statements)

References 39 publications

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“…We feel that our continuous time model share important features with the models of [23,54,62]. As in [23,54,62], we too observe in our model an intermittent behaviour when a state stable for relatively long time changes suddenly to a new state, which can be quite different in terms of its set of strategies that have a significant population share relative to the noise level. As in [23,54,62], our model is not confined to the interior of the simplex.…”

Section: Intermittent Dynamics On Large Graphsmentioning

confidence: 52%

“…Section 3 uses a transformation to map it into the Langevin equation on a sphere and exploits the structure therein to analyze the small noise asymptotics. Section 4 specializes the results to the case of quadratic potentials on graphs and makes some relevant observations for this special case which has important applications such as the study of the intermittent behaviour in complex large-scale systems [23], [54], [62] and clique detection problem [4], [10], [11], [12]. Section 5 presents some numerical experiments to support the theoretical findings.…”

Section: Introductionmentioning

confidence: 94%

“…We know at least two important applications motivating such a setting. The first motivation comes from the Tangled Nature model [23] or its high level abstraction based on replicator dynamics [54,62]. These models have been proposed to explain the intermittent behaviour of complex ecological systems as well as sudden, fundamental changes in economic systems.…”

Section: Intermittent Dynamics On Large Graphsmentioning

confidence: 99%

“…These models have been proposed to explain the intermittent behaviour of complex ecological systems as well as sudden, fundamental changes in economic systems. The authors of [54,62] considered a discretized version of the standard replicator dynamics with matrix M representing a large weighted random graph. They add to the standard replicator dynamics the processes of extinction and mutation.…”

Section: Intermittent Dynamics On Large Graphsmentioning

confidence: 99%

See 3 more Smart Citations

Metastability in Stochastic Replicator Dynamics

Avrachenkov¹,

Borkar²

2018

Dyn Games Appl

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We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models of stochastic replicator dynamics studied earlier. In particular, it is ill-posed due to non-uniqueness of solutions, but is amenable to a natural selection principle that picks a unique solution. The model allows us to make specific statements regarding metastable states such as small noise asymptotics for mean exit times from their domain of attraction, and quasi-stationary measures. We illustrate the general results by specializing them to replicator dynamics on graphs and demonstrate that the numerical experiments support theoretical predictions.

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Section: Intermittent Dynamics On Large Graphsmentioning

confidence: 52%

Section: Introductionmentioning

confidence: 94%

Section: Intermittent Dynamics On Large Graphsmentioning

confidence: 99%

Section: Intermittent Dynamics On Large Graphsmentioning

confidence: 99%

See 2 more Smart Citations

Metastability in Stochastic Replicator Dynamics

Avrachenkov¹,

Borkar²

2018

Dyn Games Appl

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“…Here we briefly present the intermittent behavior of the Replicator Model with Mutations, details of which can be found in [6]. The replicator equation [9] was introduced in evolutionary game theory in order to capture the frequency-dependent nature of the evolution process.…”

Section: The Replicator Model With Mutationsmentioning

confidence: 99%

Relating high dimensional stochastic complex systems to low-dimensional intermittency

Diaz-Ruelas

Piovani

Robledo

2017

Eur. Phys. J. Spec. Top.

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We evaluate the implication and outlook of an unanticipated simplification in the macroscopic behavior of two high-dimensional sto-chastic models: the Replicator Model with Mutations and the Tangled Nature Model (TaNa) of evolutionary ecology. This simplification consists of the apparent display of low-dimensional dynamics in the nonstationary intermittent time evolution of the model on a coarse-grained scale. Evolution on this time scale spans generations of individuals, rather than single reproduction, death or mutation events. While a local one-dimensional map close to a tangent bifurcation can be derived from a mean-field version of the TaNa model, a nonlinear dynamical model consisting of successive tangent bifurcations generates time evolution patterns resembling those of the full TaNa model. To advance the interpretation of this finding, here we consider parallel results on a game-theoretic version of the TaNa model that in discrete time yields a coupled map lattice. This in turn is represented, a la Langevin, by a onedimensional nonlinear map. Among various kinds of behaviours we obtain intermittent evolution associated with tangent bifurcations. We discuss our results.

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Structure-based identification of sensor species for anticipating critical transitions

Aparicio

Hernández

Moog

et al. 2021

Proc. Natl. Acad. Sci. U.S.A.

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Ecological systems can undergo sudden, catastrophic changes known as critical transitions. Anticipating these critical transitions remains challenging in systems with many species because the associated early warning signals can be weakly present or even absent in some species, depending on the system dynamics. Therefore, our limited knowledge of ecological dynamics may suggest that it is hard to identify those species in the system that display early warning signals. Here, we show that, in mutualistic ecological systems, it is possible to identify species that early anticipate critical transitions by knowing only the system structure—that is, the network topology of plant–animal interactions. Specifically, we leverage the mathematical theory of structural observability of dynamical systems to identify a minimum set of “sensor species,” whose measurement guarantees that we can infer changes in the abundance of all other species. Importantly, such a minimum set of sensor species can be identified by using the system structure only. We analyzed the performance of such minimum sets of sensor species for detecting early warnings using a large dataset of empirical plant–pollinator and seed-dispersal networks. We found that species that are more likely to be sensors tend to anticipate earlier critical transitions than other species. Our results underscore how knowing the structure of multispecies systems can improve our ability to anticipate critical transitions.

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Linear stability theory as an early warning sign for transitions in high dimensional complex systems

Cited by 11 publications

References 39 publications

Metastability in Stochastic Replicator Dynamics

Metastability in Stochastic Replicator Dynamics

Relating high dimensional stochastic complex systems to low-dimensional intermittency

Structure-based identification of sensor species for anticipating critical transitions

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