WIAS Preprint No. 2417, (2017)

Stability of spiral chimera states on a torus



Authors

  • Omel'chenko, Oleh E.
    ORCID: 0000-0003-0526-1878
  • Wolfrum, Matthias
  • Knobloch, Edgar

2010 Mathematics Subject Classification

  • 34C15 37G35 34D06 35B36

Keywords

  • Coupled oscillators, coherence-incoherence patterns, chimera states, Ott--Antonsen equation, bifurcation analysis

DOI

10.20347/WIAS.PREPRINT.2417

Abstract

We study destabilization mechanisms of spiral coherence-incoherence patterns known as spiral chimera states that form on a two-dimensional lattice of nonlocally coupled phase oscillators. For this purpose we employ the linearization of the Ott--Antonsen equation that is valid in the continuum limit and perform a detailed two-parameter stability analysis of a $D_4$-symmetric chimera state, i.e., a four-core spiral state. We identify fold, Hopf and parity-breaking bifurcations as the main mechanisms whereby spiral chimeras can lose stability. Beyond these bifurcations we find new spatio-temporal patterns, in particular, quasiperiodic chimeras, $D_2$-symmetric spiral chimeras as well as drifting states.

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