Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

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

doi:10.1063/5.0039879

Cited by 24 publications

(10 citation statements)

References 44 publications

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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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“…The coupling through the mean-field in an ensemble of identical coupled oscillators can provide fascinating outcomes like explosive death [75] and synchronous state [76]. We consider the following equations…”

Section: Mechanism Involved In the Formation Of Extreme Eventsmentioning

confidence: 99%

Extreme events in globally coupled chaotic maps

Chowdhury,

Ray,

Mishra

et al. 2021

Preprint

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Understanding and predicting uncertain things are the central themes of scientific evolution. Human beings revolve around these fears of uncertainties concerning various aspects like a global pandemic, health, finances, to name but a few. Dealing with this unavoidable part of life is far tougher due to the chaotic nature of these unpredictable activities. In the present article, we consider a global network of identical chaotic maps, which splits into two different clusters, despite the interaction between all nodes are uniform. The stability analysis of the spatially homogeneous chaotic solutions provides a critical coupling strength, before which we anticipate such partial synchronization. The distance between these two chaotic synchronized populations often deviates more than eight times of standard deviation from its long-term average. The probability density function of these highly deviated values fits well with the Generalized Extreme Value distribution. Meanwhile, the distribution of recurrence time intervals between extreme events resembles the Weibull distribution. The existing literature helps us to characterize such events as extreme events using the significant height. These extremely high fluctuations are less frequent in terms of their occurrence. We determine numerically a range of coupling strength for these extremely large but recurrent events. On-off intermittency is the responsible mechanism underlying the formation of such extreme events. Besides understanding the generation of such extreme events and their statistical signature, we furnish forecasting these events using the powerful deep learning algorithms of an artificial recurrent neural network. This Long Short-Term Memory (LSTM) can offer handy one-step forecasting of these chaotic intermittent bursts. We also ensure the robustness of this forecasting model with two hundred hidden cells in each LSTM layer.

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“…Subsequently, the explosive amplitude death, as another type of ED, emerged in an ensemble of N indirectly coupled and identical SL oscillators through a common dynamic environment [13], indicating that all oscillators settle on the same fixed point suddenly. Moreover, ED also occurs under the other coupling mechanisms, such as mean-field diffusion [23], conjugate variables coupling [24], quorum sensing [25], and state-space-dependent dynamic interactions [26].…”

Section: Introductionmentioning

confidence: 99%

Frequency-amplitude correlation inducing first-order phase transition in coupled oscillators

Wang

2022

New J. Phys.

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The first-order phase transitions in coupled oscillators have been widely studied because of their discontinuity and irreversibility. In previous research, the designed coupling mechanisms between each pair of oscillators can cause the first-order phase transitions occur stably. In the present study, we propose a new mechanism which requires the existence of an inversely proportional relationship between the natural frequencies and the intrinsic amplitudes in the homogeneously coupled oscillators. Based on two classical oscillator models, i.e., the Poincaré model and the Stuart-Landau model, the emergence of explosive oscillation death is independent of the frequency distribution. Our findings indicate that the first-order phase transitions can be induced by the frequency-amplitude correlation for the first time . Therefore, it provides a novel perspective to understand explosive phenomena in coupled oscillators.

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Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions

Cited by 24 publications

References 44 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

Extreme events in globally coupled chaotic maps

Frequency-amplitude correlation inducing first-order phase transition in coupled oscillators

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