Amplitude death in nonlinear oscillators with nonlinear coupling

Prasad, Awadhesh; Dhamala, Mukesh; Adhikari, Bhim M.; Ramaswamy, Ramakrishna

doi:10.1103/physreve.81.027201

Cited by 119 publications

(81 citation statements)

References 26 publications

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“…8 is the largest two Lyapunov exponents for identical oscillators as a function of ε, the region where all Lyapunov exponents are negative corresponds to amplitude death (the transients are shown in the inset). We have found that the phenomenon of amplitude death when systems are coupled through nonlinear interactions is very general and occurs in the absence of parameter mismatch, in the absence of time-delay (although time delay can enhance the effect) [15,76].…”

Section: Nonlinear Couplingmentioning

confidence: 99%

“…An interesting extension that uses nonlinear coupling makes it possible to not only achieve AD, but also to specify the steady state of the coupled system [15,21]. We will illustrate the targeting of specific fixed points in Sec.…”

Section: Nonlinear Couplingmentioning

confidence: 99%

“…The motivation for this choice of function is discussed in Sec. 3.1, and is common in neuronal systems [15,21]. Fig.…”

Section: Nonlinear Couplingmentioning

confidence: 99%

“…Different situations where amplitude death occurs have been described, and it is now known that the phenomenon can be seen when the interacting systems are identical [7,11,12,13], mismatched [1,6], when the coupling is dynamical [14], or nonlinear (nondiffusive) [15]. We review these various situations and also discuss the general mechanism for AD in Sec.…”

Section: Introductionmentioning

confidence: 99%

“…The occurrence of AD in networks of coupled oscillators [15,29,30,31,32,33,34,35] is another topic of considerable current relevance. Studies have been carried out for a variety of network topologies, ranging from systems coupled on a ring [36,37], as well as in the so-called small world [38] and scale-free networks [39].…”

Section: Introductionmentioning

confidence: 99%

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Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

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Section: Nonlinear Couplingmentioning

confidence: 99%

Section: Nonlinear Couplingmentioning

confidence: 99%

“…The motivation for this choice of function is discussed in Sec. 3.1, and is common in neuronal systems [15,21]. Fig.…”

Section: Nonlinear Couplingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

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Environmentally Induced Chaos and Amplitude Death in Neuronal Network Activity

Pankratova

2021

NODYCON Conference Proceedings Series

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Cycle-Star Motifs: Network Response to Link Modifications

Bakrani,

Kiran,

Eroglu

et al. 2024

J Nonlinear Sci

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Understanding efficient modifications to improve network functionality is a fundamental problem of scientific and industrial interest. We study the response of network dynamics against link modifications on a weakly connected directed graph consisting of two strongly connected components: an undirected star and an undirected cycle. We assume that there are directed edges starting from the cycle and ending at the star (master–slave formalism). We modify the graph by adding directed edges of arbitrarily large weights starting from the star and ending at the cycle (opposite direction of the cutset). We provide criteria (based on the sizes of the star and cycle, the coupling structure, and the weights of cutset and modification edges) that determine how the modification affects the spectral gap of the Laplacian matrix. We apply our approach to understand the modifications that either enhance or hinder synchronization in networks of chaotic Lorenz systems as well as Rössler. Our results show that the hindrance of collective dynamics due to link additions is not atypical as previously anticipated by modification analysis and thus allows for better control of collective properties.

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Amplitude death in nonlinear oscillators with nonlinear coupling

Cited by 119 publications

References 26 publications

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Amplitude death: The emergence of stationarity in coupled nonlinear systems

Environmentally Induced Chaos and Amplitude Death in Neuronal Network Activity

Cycle-Star Motifs: Network Response to Link Modifications

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