Chaotic weak chimeras and their persistence in coupled populations of phase oscillators

Christian Bick, Peter Ashwin

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

Nontrivial collective behavior may emerge from the interactive dynamics of many oscillatory units. Chimera states are chaotic patterns of spatially localized coherent and incoherent oscillations. The recently-introduced notion of a weak chimera gives a rigorously testable characterization of chimera states for finite-dimensional phase oscillator networks. In this paper we give some persistence results for dynamically invariant sets under perturbations and apply them to coupled populations of phase oscillators with generalized coupling. In contrast to the weak chimeras with nonpositive maximal Lyapunov exponents constructed so far, we show that weak chimeras that are chaotic can exist in the limit of vanishing coupling between coupled populations of phase oscillators. We present numerical evidence that positive Lyapunov exponents can persist for a positive measure set of this inter-population coupling strength.

Original languageEnglish
Pages (from-to)1468-1486
Number of pages19
JournalNonlinearity
Volume29
Issue number5
DOIs
Publication statusPublished - 29 Mar 2016
Externally publishedYes

Keywords

  • chaotic dynamics
  • chimera states
  • persistence
  • phase oscillators

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