Spiral wave chimeras in locally coupled oscillator systems

Li, Bingwei; Dierckx, Hans

doi:10.1103/physreve.93.020202

Cited by 64 publications

(35 citation statements)

References 34 publications

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“…When the nonlocality level is low (small values of the coupling range), the system demonstrates complex spatiotemporal structures, namely spiral wave and target wave chimeras as in [7]. The features of the spiral wave chimeras are similar to the ones in the other models [7,17,42,22,40,15]. For example, there is no characteristic bell-like spatial distribution of the mean oscillation frequency.…”

Section: Discussionmentioning

confidence: 88%

Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

Shepelev

Bukh

Muni

et al. 2020

Chaos, Solitons & Fractals

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The behaviour of the ensemble of coupled van der Pol oscillators is abundant when coupling parameters are changed. Incoherent and chimeralike regimes are observed at small values of the coupling strength parameter. Synchronization takes place with increasing of the coupling strength and coupling range parameters. Various chimera and solitary states are realised when the coupling strength parameter is sufficiently large. The single van der Pol oscillator is taken in the regime of relaxation oscillations. Therefore, the lattice may realise spiral wave and spiral wave chimera regimes. Besides, target wave and solitary state regimes are observed in the ensemble. Finally, the solitary state and solitary state chimera regimes are firstly shown for the lattice of coupled van der Pol oscillators.

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Section: Discussionmentioning

confidence: 88%

Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

Shepelev

Bukh

Muni

et al. 2020

Chaos, Solitons & Fractals

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“…• Although we have only discussed systems with nonlocal coupling, it has recently been found that systems with just local coupling can also support chimera states [27,32]. A self-consistency derivation of the form in [27] may be possible for spiral waves in locally coupled two-dimensional networks, and solutions of the resulting self-consistency equation might be followed using the same techniques used in this paper.…”

Section: And 22)?mentioning

confidence: 99%

Chimeras in Two-Dimensional Domains: Heterogeneity and the Continuum Limit

Laing¹

2017

SIAM J. Appl. Dyn. Syst.

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We consider three different two-dimensional networks of nonlocally coupled heterogeneous phase oscillators. These networks were previously studied with identical oscillators and a number of spatiotemporal patterns found, mostly as a result of direct numerical simulation. Here we take the continuum limit of an infinite number of oscillators and use the Ott/Antonsen ansatz to derive continuum level evolution equations for order parameter-like quantities. Most of the patterns previously found in these networks correspond to relative fixed points of these evolution equations, and we show here the results of extensive numerical investigations of these fixed points: their existence and stability, and the bifurcations involved in their loss of stability as parameters are varied. Our results answer a number of questions posed by previous authors who studied these networks, and provide a better understanding of these networks' dynamics.

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“…Recently, various synchronization scenarios in multiplex and multilayer [23][24][25][26][27][28][29][30][31] networks were studied, such as generalized synchronization [32], inter-layer (external and mutual) synchronization [33][34][35][36][37][38], relay (remote) synchronization [39,40], explosive synchronization [41][42][43][44]. Among a large variety of chimera states [35,, here we concentrate on so-called "spiral wave chimera structures" which are observed in 2D ensembles of coupled nonlinear oscillators [10,22,[73][74][75][76][77][78][79][80][81][82][83][84][85][86]. These were typically found in the case of nonlocal coupling topology of network elements.…”

Section: Introductionmentioning

confidence: 99%

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

Bukh¹,

Strelkova²,

Анищенко³

2019

ISUNSSP

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The paper describes the spatio-temporal dynamics of a lattice that is given by a 2D N × N network of nonlocally coupled Nekorkin maps which model neuronal activity. The network behavior is studied for periodic and no-flux boundary conditions. It is shown that for certain values of the coupling parameters, rotating spiral waves and spiral wave chimeras can be observed in the considered lattice. We analyze and compare statistical and dynamical characteristics of the local oscillators from coherence and incoherence clusters of a spiral wave chimera. Furthermore, effects of mutual and external synchronization of spiral wave structures in two coupled such lattices are studied. We show numerically that spiral wave structures, including spiral wave chimeras, can be synchronized and establish the mechanism of their synchronization. Our numerical studies indicate that when the coupling strength between the lattices is sufficiently weak, only a certain part of oscillators of the interacting networks is imperfectly synchronized, while the other part demonstrates a partially synchronous behavior. If the spatiotemporal patterns in the lattices do not include incoherent cores, imperfect synchronization is realized for most oscillators above a certain value of the coupling strength. In the regime of spiral wave chimeras, the imperfect synchronization of all oscillators cannot be achieved even for sufficiently large values of the coupling strength.

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Spiral wave chimeras in locally coupled oscillator systems

Cited by 64 publications

References 34 publications

Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

Role of solitary states in forming spatiotemporal patterns in a 2D lattice of van der Pol oscillators

Chimeras in Two-Dimensional Domains: Heterogeneity and the Continuum Limit

Spiral Wave Patterns in Two-Layer 2D Lattices of Nonlocally Coupled Discrete Oscillators. Synchronization of Spiral Wave Chimeras

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