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Nelin. Dinam., 2018, Volume 14, Number 4, Pages 419–433 (Mi nd623)  

This article is cited in 3 scientific papers (total in 3 papers)

Nonlinear physics and mechanics

Synchronization of Chimera States in Coupled Networks of Nonlinear Chaotic Oscillators

A. V. Bukh, G. I. Strelkova, V. S. Anishchenko

Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia

Abstract: Effects of synchronization of chimera states are studied numerically in a two-layer network of nonlocally coupled nonlinear chaotic discrete-time systems. Each layer represents a ring of nonlocally coupled logistic maps in the chaotic mode. A control parameter mismatch is introduced to realize distinct spatiotemporal structures in isolated ensembles. We consider external synchronization of chimeras for unidirectional intercoupling and mutual synchronization in the case of bidirectional intercoupling. Synchronization is quantified by calculating the crosscorrelation coefficient between the symmetric elements of the interacting networks. The same quantity is used to determine finite regions of synchronization inside which the cross-correlation coefficient is equal to 1. The identity of synchronous structures and the existence of finite synchronization regions are necessary and sufficient conditions for establishing the synchronization effect. It is also shown that our results are qualitatively similar to the synchronization of periodic self-sustained oscillations.

Keywords: multilayer networks, nonlocal coupling, chimera states, synchronization

Funding Agency Grant Number
Deutsche Forschungsgemeinschaft SFB 910
Russian Science Foundation 16-12-10175
This work was supported by DFG in the framework of SFB 910, by the Russian Ministry of Education and Science (Project Code 3.8616.2017) and by the Russian Science Foundation (grant No. 16-12-10175).


DOI: https://doi.org/10.20537/nd180401

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MSC: 90B10, 34D06, 35B36
Received: 19.09.2018
Accepted:22.10.2018
Language:

Citation: A. V. Bukh, G. I. Strelkova, V. S. Anishchenko, “Synchronization of Chimera States in Coupled Networks of Nonlinear Chaotic Oscillators”, Nelin. Dinam., 14:4 (2018), 419–433

Citation in format AMSBIB
\Bibitem{BukStrAni18}
\by A. V. Bukh, G. I. Strelkova, V. S. Anishchenko
\paper Synchronization of Chimera States in Coupled Networks of Nonlinear Chaotic Oscillators
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 4
\pages 419--433
\mathnet{http://mi.mathnet.ru/nd623}
\crossref{https://doi.org/10.20537/nd180401}
\elib{https://elibrary.ru/item.asp?id=36686066}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Bukh, E. Schoell, V. S. Anishchenko, “Synchronization of spiral wave patterns in two-layer 2D lattices of nonlocally coupled discrete oscillators”, Chaos, 29:5 (2019), 053105  crossref  mathscinet  zmath  isi  scopus
    2. M. Mikhaylenko, L. Ramlow, S. Jalan, A. Zakharova, “Weak multiplexing in neural networks: switching between chimera and solitary states”, Chaos, 29:2 (2019), 023122  crossref  mathscinet  zmath  isi  scopus
    3. G. I. Strelkova, V. S. Anishchenko, “Spatio-temporal structures in ensembles of coupled chaotic systems”, Phys. Usp., 63:2 (2020), 145–161  mathnet  crossref  crossref  isi  elib
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