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Nonlinear Dynamics

, Volume 90, Issue 4, pp 2317–2330 | Cite as

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

  • Igor A. ShepelevEmail author
  • Andrei V. Bukh
  • Galina I. Strelkova
  • Tatiana E. Vadivasova
  • Vadim S. Anishchenko
Original Paper

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.

Keywords

Ensemble of oscillators Spatial structure Chimera Dynamical chaos Nonlocal coupling FitzHugh–Nagumo oscillator 

Mathematics Subject Classification

34G20 37N30 

Notes

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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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Igor A. Shepelev
    • 1
    Email author
  • Andrei V. Bukh
    • 1
  • Galina I. Strelkova
    • 1
  • Tatiana E. Vadivasova
    • 1
  • Vadim S. Anishchenko
    • 1
  1. 1.Saratov National Research State UniversitySaratovRussia

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