Cite this article as:

Anishchenko V. S., Kholuianova I. А., Bogomolov S. А. Synchronization of Chimera States in Ensembles of Nonlocally Coupled Cubic Maps. Izvestiya of Saratov University. New series. Series Physics, 2018, vol. 18, iss. 2, pp. 103-111. DOI: https://doi.org/10.18500/1817-3020-2018-18-2-103-111


UDC: 
537.86:530.182
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Russian

Synchronization of Chimera States in Ensembles of Nonlocally Coupled Cubic Maps

Abstract

Background and Objectives: Effects of mutual and external synchronization of chimera states are studied in two coupled ensembles of discrete maps. Each of the ensembles is a onedimensional ring of nonlocally coupled cubic maps in the chaotic oscillation mode. In order to create differences in the dynamics of the ensembles when there is no coupling between them, a mismatch is introduced in the parameters of the individual oscillators of the first and second rings. Effects of external and mutual synchronization of chimera states are explored in detail.

Materials and Methods: The effect of synchronization of spatio-temporal structures in two coupled ensembles of discrete nonlinear oscillators is studied numerically. The identity of synchronous structures and synchronization regions was quantified by of calculating the cross-correlation coefficient between the corresponding oscillators of interconnected ensembles.

Results: The effects of mutual and external synchronization of chimera structures have been established and confirmed by snapshots of the amplitude of oscillations, by calculations of the cross-correlation coefficient between the respective elements of the ensembles and by plotting the synchronization regions on the coupling parameter.

Conclusions: The paper presents the numerical results which show that the realization of the effects of mutual and external synchronization of chimera states can be realized in two nonlocally coupled ensembles of cubic maps. The identity of synchronous chimera states and the presence of a finite region of synchronization in the variation of the coupling coefficient between the interacting ensembles are confirmed.

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