Chimera states in a Duffing oscillators chain coupled to nearest neighbors

Clerc, Marcel G.; Coulibaly, Saliya; Ferré, Michel; Rojas, R. G.

doi:10.1063/1.5025038

Cited by 40 publications

(18 citation statements)

References 44 publications

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“…For a long time, chimera states were believed to exist mostly for nonlocal coupling schemes. This consensus was revised when chimeras were found in systems of globally [36][37][38][39][40][41] and locally coupled oscillators [42][43][44][45][46][47]. Although these regular topologies often capture the nature of the interaction between the coupled elements, there are many real-world systems where a more complex connectivity description is required.…”

Section: Introductionmentioning

confidence: 99%

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Pournaki

Merfort

Ruiz

et al. 2019

Front. Appl. Math. Stat.

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We investigate synchronization patterns and chimera-like states in the modular multilayer topology of the connectome of Caenorhabditis elegans. In the special case of a designed network with two layers, one with electrical intra-community links and one with chemical inter-community links, chimera-like states are known to exist. Aiming at a more biological approach based on the actual connectivity data, we consider a network consisting of two synaptic (electrical and chemical) and one extrasynaptic (wireless) layers. Analyzing the structure and properties of this layered network using Multilayer-Louvain community detection, we identify modules whose nodes are more strongly coupled with each other than with the rest of the network. Based on this topology, we study the dynamics of coupled Hindmarsh-Rose neurons. Emerging synchronization patterns are quantified using the pairwise Euclidean distances between the values of all oscillators, locally within each community and globally across the network. We find a tendency of the wireless coupling to moderate the average coherence of the system: for stronger wireless coupling, the levels of synchronization decrease both locally and globally, and chimera-like states are not favored. By introducing an alternative method to define meaningful communities based on the dynamical correlations of the nodes, we obtain a structure that is dominated by two large communities. This promotes the emergence of chimera-like states and allows to relate the dynamics of the corresponding neurons to biological neuronal functions such as motor activities.

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Section: Introductionmentioning

confidence: 99%

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Pournaki

Merfort

Ruiz

et al. 2019

Front. Appl. Math. Stat.

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“…This second balance renders discrete dissipative solitons more robust 10-12 . Generally speaking, when a system exhibits a simultaneous coexistence between coherence and incoherence behavior in coupled oscillators, the resulting phenomenon is called chimera states 13 . Initially, this phenomenon was reported in the context of nonlocally coupled phase oscillators 13,14 , and extended later on to locally coupling oscillators 15,16 . In optical systems, experimental observations of chimera states have been reported using an optoelectronic delayed feedback setup 17 , laser diodes coupled to a nonlinear saturable absorber 18 , and laser diodes subjected to a coherent polarization 19 .…”

Section: Introductionmentioning

confidence: 90%

Two-dimensional optical chimera states in an array of coupled waveguide resonators

Clerc

Coulibaly

Ferré

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Two-dimensional arrays of coupled waveguides or coupled microcavities allow to confine and manipulate light. Based on a paradigmatic envelope equation, we show that these devices, subject to a coherent optical injection, support coexistence between a coherent and incoherent emission. In this regime, we show that two-dimensional chimera state can be generated. Depending on initial conditions, the system exhibits a family of two-dimensional chimera states and interaction between them. We characterize these two-dimensional structures by computing their Lyapunov spectrum, and Yorke-Kaplan dimension. Finally, we show that two-dimensional chimera states are of spatiotemporal chaotic nature.One-dimensional nonlinear coupled microcavities exhibit a rich spatiotemporal dynamics. In particular, these coupled microcavities have fully synchronized or incoherent light emission of a spatiotemporal chaotic nature. Also, depending on the initial conditions, these devices show coexistence between desynchronized and synchronized domains, often called optical chimera states. In this contribution, we show evidence of optical chimeras in a twodimensional array of coupled waveguide resonators. Due to the additional degrees of freedom, the smaller localized solutions exhibit a chaotic spatiotemporal evolutionwhich is not the case of the one-dimensional counterpart. Lyapunov spectrum and Yorke-Kaplan dimensions are calculated to characterize these intriguing localized states.

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“…The regular influence on the chimera states is also weakly studied. This issue has been investigated in [51,[56][57][58]. In [51] the harmonic influence with a certain frequency stabilizes a virtual chimera in the oscillator with delayed feedback.…”

Section: Introductionmentioning

confidence: 99%

Effects of external global harmonic influence on chimera states

Shepelev

Вадивасова

2020

Nonlinear Dyn

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The effects of the global harmonic force on an ensemble of nonlocally coupled chaotic Rössler oscillators is studied. The autonomous ensemble without external force demonstrates a stable regime of chimera state. We have considered two types of the chimera states, namely phase chimera with a single incoherence cluster and combined chimera state with the incoherence clusters of the phase and amplitude chimeras. We have shown that even the sufficiently weak external influence leads to the qualitative changes in the spatiotemporal behavior of the ensemble under study. The diagram of regimes has been plotted in the plane of external signal parameters, where we detect regions with different dynamical regimes, induced by the external excitation. They are the spatiotemporal intermittence of structures, stable chimera states, stable regimes with a piecewise spatial profile, spatiotemporal chaos, complete chaotic synchronization and spatial incoherence. We have explored each of these regimes in detail and has found out that they are characterized by a certain distinctive range of the maximal Lyapunov exponent. We have found that the change of spatiotemporal behavior is not accompanied by the effects of locking the natural frequency or of suppression of selfoscillation by the external signal.

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Chimera states in a Duffing oscillators chain coupled to nearest neighbors

Cited by 40 publications

References 44 publications

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Synchronization Patterns in Modular Neuronal Networks: A Case Study of C. elegans

Two-dimensional optical chimera states in an array of coupled waveguide resonators

Effects of external global harmonic influence on chimera states

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