Chimera and globally clustered chimera: Impact of time delay

Sheeba, Jane H.; Chandrasekar, V. K.; Lakshmanan, M.

doi:10.1103/physreve.81.046203

Cited by 65 publications

(20 citation statements)

References 42 publications

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“…The sparsity of induced by may yield coexisting synchronized and desynchronized groups within the network, which are often labelled chimera states in the study of phase oscillator systems. It has been found that they crucially depend on the combination of coupling strengths and phase shifts [45], [54], [55] (or delays [56]), confirming that there has to be a specific matching of coupling and delays for synchronization to occur.…”

Section: Discussionmentioning

confidence: 94%

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

2014

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The discrepancy between structural and functional connectivity in neural systems forms the challenge in understanding general brain functioning. To pinpoint a mapping between structure and function, we investigated the effects of (in)homogeneity in coupling structure and delays on synchronization behavior in networks of oscillatory neural masses by deriving the phase dynamics of these generic networks. For homogeneous delays, the structural coupling matrix is largely preserved in the coupling between phases, resulting in clustered stationary phase distributions. Accordingly, we found only a small number of synchronized groups in the network. Distributed delays, by contrast, introduce inhomogeneity in the phase coupling so that clustered stationary phase distributions no longer exist. The effect of distributed delays mimicked that of structural inhomogeneity. Hence, we argue that phase (de-)synchronization patterns caused by inhomogeneous coupling cannot be distinguished from those caused by distributed delays, at least not by the naked eye. The here-derived analytical expression for the effective coupling between phases as a function of structural coupling constitutes a direct relationship between structural and functional connectivity. Structural connectivity constrains synchronizability that may be modified by the delay distribution. This explains why structural and functional connectivity bear much resemblance albeit not a one-to-one correspondence. We illustrate this in the context of resting-state activity, using the anatomical connectivity structure reported by Hagmann and others.

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Section: Discussionmentioning

confidence: 94%

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

2014

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“…Complex chimera-like synchronization behaviour, involving the unstable formation of synchronized and desynchronized coalitions of oscillators driven by transitions between metastable states, has been demonstrated in phase-lagged Kuramoto oscillator networks under differing topologies. 15,16 While the continuous exchange of phase information between network participants present in these models is an accurate abstraction of many systems, the detailed operation of the mammalian brain, the all-or-nothing "action potentials" sent over the synapses connecting neurons, is better described by the exchange of a series of discrete events.…”

Section: Introductionmentioning

confidence: 99%

Metastability and chimera states in modular delay and pulse-coupled oscillator networks

Wildie

Shanahan

2012

Chaos: An Interdisciplinary Journal of Nonlinear Science

118

107

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Modular networks of delay-coupled and pulse-coupled oscillators are presented, which display both transient (metastable) synchronization dynamics and the formation of a large number of "chimera" states characterized by coexistent synchronized and desynchronized subsystems. We consider networks based on both community and small-world topologies. It is shown through simulation that the metastable behaviour of the system is dependent in all cases on connection delay, and a critical region is found that maximizes indices of both metastability and the prevalence of chimera states. We show dependence of phase coherence in synchronous oscillation on the level and strength of external connectivity between communities, and demonstrate that synchronization dynamics are dependent on the modular structure of the network. The long-term behaviour of the system is considered and the relevance of the model briefly discussed with emphasis on biological and neurobiological systems.

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“…An ensemble of coupled oscillators is a veritable black box exhibiting a plethora of complex cooperative dynamical behaviors mimicking several real world phenomena [1,2,3,4]. Chimera state is such an intriguing emerging behavior that has been identified in an ensemble of identical oscillators with non-local coupling [5,6,7,8,9,10,11,12,13,14,15]. Since its identification, the notion of chimera has provoked a flurry of intense investigations because of the surprising fact that such an ensemble splits into two dynamically distinct domains, wherein all the oscillators evolve in synchrony in the coherent domain, while the oscillators in the incoherent domain evolve in asynchrony [16,17,18].…”

Section: Introductionmentioning

confidence: 99%

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

Gopal¹,

Chandrasekar²,

Senthilkumar³

et al. 2018

Communications in Nonlinear Science and Numerical Simulation

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A complex collective emerging behavior characterized by coexisting coherent and incoherent domains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and complete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.

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Chimera and globally clustered chimera: Impact of time delay

Cited by 65 publications

References 42 publications

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

Structure-Function Discrepancy: Inhomogeneity and Delays in Synchronized Neural Networks

Metastability and chimera states in modular delay and pulse-coupled oscillator networks

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

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