Dynamic interaction induced explosive death

Dixit, Shiva; Chowdhury, Sayantan Nag; Ghosh, Dibakar; Shrimali, Manish Dev

doi:10.1209/0295-5075/133/40003

Cited by 28 publications

(13 citation statements)

References 62 publications

(93 reference statements)

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“…The stationary states are interpreted using the gametheoretic concepts of the Nash equilibrium and the evolutionarily stable strategy. The emergence of stationary states on coupled systems [91][92][93][94][95][96][97] also attracts numerous researchers of nonlinear dynamics due to their multiple practical applications.…”

Section: Introductionmentioning

confidence: 99%

Complex evolutionary dynamics due to punishment and free space in ecological multigames

et al. 2021

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The concurrence of ecological and evolutionary processes often arises as an integral part of various biological and social systems. We here study eco-evolutionary dynamics by adopting two paradigmatic metaphors of social dilemmas with contrasting outcomes. We use the Prisoner’s Dilemma and Snowdrift games as the backbone of the proposed mathematical model. Since cooperation is a costly proposition in the face of the Darwinian theory of evolution, we go beyond the traditional framework by introducing punishment as an additional strategy. Punishers bare an additional cost from their own resources to try and discourage or prohibit free-riding from selfish defectors. Our model also incorporates the ecological signature of free space, which has an altruistic-like impact because it allows others to replicate and potentially thrive. We show that the consideration of these factors has broad implications for better understanding the emergent complex evolutionary dynamics. In particular, we report the simultaneous presence of different subpopulations through the spontaneous emergence of cyclic dominance, and we determine various stationary points using traditional game-theoretic concepts and stability analysis.

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Section: Introductionmentioning

confidence: 99%

Complex evolutionary dynamics due to punishment and free space in ecological multigames

et al. 2021

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“…Thus, to provide a rigorous mathematical classification of the underlying bifucations one would have to follow an alternative, albeit mean field approach. Recently, for example, Dixit et al ( 2021 ) has developed such a mean field approach that facilitates the use of sophisticated numerical continuation software (XPPAUT), to obtain the full bifurcation structure. A similar analysis of the present system could be a fruitful topic for future research.…”

Section: Resultsmentioning

confidence: 99%

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

Botha

Ansariara

Emadi

et al. 2022

Front. Comput. Neurosci.

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The union of the Kuramoto–Sakaguchi model and the Hebb dynamics reproduces the Lisman switch through a bistability in synchronized states. Here, we show that, within certain ranges of the frustration parameter, the chimera pattern can emerge, causing a different, time-evolving, distribution in the Hebbian synaptic strengths. We study the stability range of the chimera as a function of the frustration (phase-lag) parameter. Depending on the range of the frustration, two different types of chimeras can appear spontaneously, i.e., from randomized initial conditions. In the first type, the oscillators in the coherent region rotate, on average, slower than those in the incoherent region; while in the second type, the average rotational frequencies of the two regions are reversed, i.e., the coherent region runs, on average, faster than the incoherent region. We also show that non-stationary behavior at finite N can be controlled by adjusting the natural frequency of a single pacemaker oscillator. By slowly cycling the frequency of the pacemaker, we observe hysteresis in the system. Finally, we discuss how we can have a model for learning and memory.

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“…Recent studies establish sudden transitions and tipping in such systems, like explosive synchronisation and explosive death, multiplex induced critical transitions etc. [196,197,198]. While the order parameters and other characteristics in such transitions are well studied, a possible EWS for these transitions remain elusive.…”

Section: Discussionmentioning

confidence: 99%

Early warning signals for critical transitions in complex systems

George¹,

Kachhara²,

Ambika³

2021

Preprint

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In this review, we present the different measures of early warning signals that can indicate the occurrence of critical transitions in complex systems. We start with the mechanisms that trigger critical transitions, how they relate to warning signals and the methods used to detect early warning signals (EWS) for sudden transitions or tipping. We discuss briefly a few applications in real systems in this context, like transitions in ecology, climate and environment, medicine, epidemics, finance and engineering. Towards the end, we mention the issues in detecting EWS in specific applications and our perspective on future trends in this area, especially related to sudden transitions in the dynamics of connected systems on complex networks.

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Dynamic interaction induced explosive death

Cited by 28 publications

References 62 publications

Complex evolutionary dynamics due to punishment and free space in ecological multigames

Complex evolutionary dynamics due to punishment and free space in ecological multigames

Chimera Patterns of Synchrony in a Frustrated Array of Hebb Synapses

Early warning signals for critical transitions in complex systems

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