Synchronization of Chimera States in Coupled Networks of Nonlinear Chaotic Oscillators

    Received 19 September 2018; accepted 19 October 2018

    2018, Vol. 14, no. 4, pp.  419-433

    Author(s): Bukh A. V., Strelkova G. I., Anishchenko V. S.

    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
    Citation: Bukh A. V., Strelkova G. I., Anishchenko V. S., Synchronization of Chimera States in Coupled Networks of Nonlinear Chaotic Oscillators, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 4, pp.  419-433

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