WIAS Preprint No. 1777, (2013)

Coherence-incoherence patterns in a ring of non-locally coupled phase oscillators


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

2010 Mathematics Subject Classification

  • 34C15 35B36 5B32 35B42 35Q83

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt, 89.75.Kd


  • coupled phase oscillators, non-local coupling, coherence-incoherence patterns, chimera states, bifurcation analysis, pattern formation


We consider a paradigmatic spatially extended model of non-locally coupled phase oscillators which are uniformly distributed within a one-dimensional interval and interact depending on the distance between their sites modulo periodic boundary conditions. This model can display peculiar spatio-temporal patterns consisting of alternating patches with synchronized (coherent) or irregular (incoherent) oscillator dynamics, hence the name coherence-incoherence pattern, or chimera state. For such patterns we formulate a general bifurcation analysis scheme based on a hierarchy of continuum limit equations. This gives us possibility to classify known coherence-incoherence patterns and to suggest directions for searching new ones.

Appeared in

  • Nonlinearity, 26 (2013) pp. 2469--2498.

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