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.
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).
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
\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}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85061715694}
Linking options:
https://www.mathnet.ru/eng/nd623
https://www.mathnet.ru/eng/nd/v14/i4/p419
This publication is cited in the following 12 articles:
I.A. Shepelev, A.V. Bukh, G.I. Strelkova, “Anti-phase synchronization of waves in a multiplex network of van der Pol oscillators”, Chaos, Solitons & Fractals, 162 (2022), 112447
J. Sawicki, J. M. Koulen, E. Schoell, “Synchronization scenarios in three-layer networks with a hub”, Chaos, 31:7 (2021), 073131
I. A. Shepelev, S. S. Muni, E. Schoell, G. I. Strelkova, “Repulsive inter-layer coupling induces anti-phase synchronization”, Chaos, 31:6 (2021), 063116
E. V. Rybalova, A. Zakharova, G. I. Strelkova, “Interplay between solitary states and chimeras in multiplex neural networks”, Chaos Solitons Fractals, 148 (2021), 111011
Ch. Du, L. Liu, Zh. Zhang, Sh. Yu, “A coupling method of double memristors and analysis of extreme transient behavior”, Nonlinear Dyn., 104:1 (2021), 765–787
I. A. Shepelev, A. V. Bukh, G. I. Strelkova, V. S. Anishchenko, “Anti-phase relay synchronization of wave structures in a heterogeneous multiplex network of 2D lattices”, Chaos Solitons Fractals, 143 (2021), 110545
E. V. Rybalova, G. I. Strelkova, V. S. Anishchenko, “Impact of sparse inter-layer coupling on the dynamics of a heterogeneous multilayer network of chaotic maps”, Chaos Solitons Fractals, 142 (2021), 110477
G. I. Strelkova, V. S. Anishchenko, “Spatio-temporal structures in ensembles of coupled chaotic systems”, Phys. Usp., 63:2 (2020), 145–161
E. Rybalova, G. Strelkova, E. Schoell, V. Anishchenko, “Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps”, Chaos, 30:6 (2020)
A. V. Bukh, V. S. Anishchenko, “Spiral and target wave chimeras in a 2D network of nonlocally coupled Van der Pol oscillators”, Chaos Solitons Fractals, 131 (2020), 109492
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
M. Mikhaylenko, L. Ramlow, S. Jalan, A. Zakharova, “Weak multiplexing in neural networks: switching between chimera and solitary states”, Chaos, 29:2 (2019), 023122
Citation in format AMSBIB
Contact us: