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Chimera states in ensembles of bistable elements with regular and chaotic dynamics

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Abstract

We consider ensembles of bistable elements with nonlocal interaction. It is shown that the bistability of units in the case of nonlocal interaction leads to the formation of chimera structures of a special type, which we have called double-well chimeras. Their distinctive feature consists in the formation of incoherence clusters with an irregular distribution of elements between two attractive sets existing in an individual element (two “potential wells”). Ensembles of different bistable units are considered, namely ensembles of cubic maps, FitzHugh–Nagumo oscillators in the regime of two stable equilibrium points and Chua’s circuits. The spatiotemporal behavior of the ensembles is studied in the cases of regular and chaotic dynamics in time, and different types of chimera structures are revealed.

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Acknowledgements

Sections 2 and 4 were supported by the Russian Science Foundation (Grant No. 16-12-10175). Sections 1 and 3 were supported by the Russian Science Foundation (Grant No. 16-12-10175). This research was partly supported in the framework of SFB910. I. A. Sh. acknowledge support from the Russian Science Foundation (Grant No. 16-12-10175).

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  1. Saratov National Research State University, Astrakhanskaya Street 83, Saratov, Russia, 410012

    Igor A. Shepelev, Andrei V. Bukh, Galina I. Strelkova, Tatiana E. Vadivasova & Vadim S. Anishchenko

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  1. Igor A. Shepelev
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  2. Andrei V. Bukh
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  3. Galina I. Strelkova
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Correspondence to Igor A. Shepelev.

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Shepelev, I.A., Bukh, A.V., Strelkova, G.I. et al. Chimera states in ensembles of bistable elements with regular and chaotic dynamics. Nonlinear Dyn 90, 2317–2330 (2017). https://doi.org/10.1007/s11071-017-3805-6

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