Critical visit to the chimera world

Ferré, Michel

doi:10.1016/j.chaos.2022.112991

Cited by 2 publications

(3 citation statements)

References 115 publications

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“…Since we suppose that this system has a finite number of solutions, by Bézout's Theorem, it has at most d N p solutions (see for instance [11]). Now, let x be a solution of (13). Then, any permutation σ(x) of the components of x is also a solution, since for our system we have σ…”

Section: On the Attractors Of Chimera Statesmentioning

confidence: 99%

“…, N }, then σ(x) ̸ = x for every permutation σ(x). Therefore, (13) has at least N ! different solutions and d N p ≥ N !, which contradicts (12).…”

Section: On the Attractors Of Chimera Statesmentioning

confidence: 99%

“…Originally identified in theoretical models of coupled oscillators [1,23], chimera states have also found empirical analog in experiments involving chemical and mechanical oscillator networks [14,24,30]. More generally, chimeras have been reported across a wide spectrum of models encompassing discrete and continuous time dynamics (for comprehensive reviews, see references [6,13,25]).…”

Section: Introductionmentioning

confidence: 99%

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Transverse Lyapunov Exponent and Chimeras in Globally Coupled Maps

Caby,

Guiraud

2024

SIAM J. Appl. Dyn. Syst.

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We study the stability properties and the long-term dynamics of chimeras in systems of globally coupled maps. In particular, we establish a formula for the transverse Lyapunov exponent of the states of the system containing synchronized units. We use this formula to present numerical evidence of attracting chimeras having chaotic dynamics, as well as periodic behaviors. We also show that, at least for polynomial local maps, attracting periodic cycles tend to belong to cluster spaces and that, more generally, the limit sets of chimeras orbits have zero Lebesgue measures for strong coupling regimes.

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Section: On the Attractors Of Chimera Statesmentioning

confidence: 99%

“…, N }, then σ(x) ̸ = x for every permutation σ(x). Therefore, (13) has at least N ! different solutions and d N p ≥ N !, which contradicts (12).…”

Section: On the Attractors Of Chimera Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Transverse Lyapunov Exponent and Chimeras in Globally Coupled Maps

Caby,

Guiraud

2024

SIAM J. Appl. Dyn. Syst.

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Chimeras in globally coupled oscillators: A review

Mishra,

Saha,

Dana

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The surprising phenomenon of chimera in an ensemble of identical oscillators is no more strange behavior of network dynamics and reality. By this time, this symmetry breaking self-organized collective dynamics has been established in many networks, a ring of non-locally coupled oscillators, globally coupled networks, a three-dimensional network, and multi-layer networks. A variety of coupling and dynamical models in addition to the phase oscillators has been used for a successful observation of chimera patterns. Experimental verification has also been done using metronomes, pendula, chemical, and opto-electronic systems. The phenomenon has also been shown to appear in small networks, and hence, it is not size-dependent. We present here a brief review of the origin of chimera patterns restricting our discussions to networks of globally coupled identical oscillators only. The history of chimeras in globally coupled oscillators is older than what has been reported in nonlocally coupled phase oscillators much later. We elaborate the story of the origin of chimeras in globally coupled oscillators in a chronological order, within our limitations, and with brief descriptions of the significant contributions, including our personal experiences. We first introduce chimeras in non-locally coupled and other network configurations, in general, and then discuss about globally coupled networks in more detail.

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Critical visit to the chimera world

Cited by 2 publications

References 115 publications

Transverse Lyapunov Exponent and Chimeras in Globally Coupled Maps

Transverse Lyapunov Exponent and Chimeras in Globally Coupled Maps

Chimeras in globally coupled oscillators: A review

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