WIAS Preprint No. 1682, (2012)

Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally coupled phase oscillators


  • Omel'chenko, Oleh
    ORCID: 0000-0003-0526-1878
  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Yanchuk, Serhiy
  • Maistrenko, Yuri
  • Sudakov, Oleksandr

2010 Mathematics Subject Classification

  • 34C15 37N20, 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt 89.75.Kd


  • phase oscillators, partial synchronization, coherence-incoherence pattern, non-local coupling




Recently it has been shown that large arrays of identical oscillators with non-local coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motion, often caled chimera states. We present here a detailed numerical study of the appearance of such solutions in two-dimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, the stationarity means that for increasing system size the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation.

Appeared in

  • Phys. Rev. E (3), 85 (2012) pp. 036210/1--036210/5.

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