WIAS Preprint No. 1618, (2011)

Chimera states are chaotic transients



Authors

  • Wolfrum, Matthias
  • Omel'chenko, Oleh
    ORCID: 0000-0003-0526-1878

2010 Mathematics Subject Classification

  • 34C15 37D45 37N20 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt, 89.75.Kd

Keywords

  • coupled phase oscillators, chaotic transients

Abstract

Spatiotemporal chaos and turbulence are universal concepts for the explanation of irregular behavior in various physical systems. Recently, a remarkable new phenomenon, called "chimera states", has been described, where in a spatially homogeneous system regions of irregular incoherent motion coexist with regular synchronized motion, forming a self organized pattern in a population of nonlocally coupled oscillators. Whereas most of the previous studies of chimera states focused their attention to the case of large numbers of oscillators employing the thermodynamic limit of infinitely many oscillators, we investigate here the properties of chimera states in populations of finite size using concepts from deterministic chaos. Our calculations of the Lyapunov spectrum show that the incoherent motion, which is described in the thermodynamic limit as a stationary behavior, in finite size systems appears as weak spatially extensive chaos. Moreover, for sufficiently small populations the chimera states reveal their transient nature: after a certain time-span we observe a sudden collapse of the chimera pattern and a transition to the completely coherent state. Our results indicate that chimera states can be considered as chaotic transients, showing the same properties as type-II supertransients in coupled map lattices.

Appeared in

  • Phys. Rev. E, 84 (2011) pp. 015201(R)/1--015201(R)/4.

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