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Chimeras and clusters in networks of hyperbolic chaotic oscillators

A. V. Cano and M. G. Cosenza

  • Grupo de Caos y Sistemas Complejos, Centro de Física Fundamental, Universidad de Los Andes, Mérida 5101, Mérida, Venezuela

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Phys. Rev. E 95, 030202(R) – Published 31 March, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.030202

Abstract

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

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Phys. Rev. E 95, 030202(R)– Published 31 March, 2017
  • Received 19 January 2017

©2017 American Physical Society

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