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    Andrei Bukh

    Astrakhanskaya 83, Saratov, 410010, Russia
    Saratov State University


    Bukh A. V., Anishchenko V. S.
    The features of external and mutual synchronization of spiral wave structures including chimera states in the interacting two-dimensional lattices of nonlocally coupled Nekorkin maps are investigated. The cases of diffusive and inertial couplings between the lattices are considered. The lattices model a neuronal activity and represent two-dimensional lattices consisting of $N \times N$ elements with $N = 200$. It is shown that the effect of complete synchronization is not achieved in the studied lattices, and only the regime of partial synchronization is realized regardless of the case of coupling between the lattices. It is important to note that the conclusion is applied not only to the regimes of spiral wave chimeras, but also to the regimes of regular spiral waves.
    Keywords: synchronization, two-dimensional lattice, spiral wave, spiral wave chimera, inertial and diffusing coupling
    Citation: Bukh A. V., Anishchenko V. S.,  Features of the Synchronization of Spiral Wave Structures in Interacting Lattices of Nonlocally Coupled Maps, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 2, pp.  243-257
    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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