WIAS Preprint No. 1908, (2013)

Partially coherent twisted states in arrays of coupled phase oscillators



Authors

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

2010 Mathematics Subject Classification

  • 34C15 37N20 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt 89.75.Kd

Keywords

  • coupled oscillators, Kuramoto model, twisted states, Ott/Antonsen, Eckhaus bifurcation

Abstract

We consider a one-dimensional array of phase oscillators with non-local coupling and a Lorentzian distribution of natural frequencies. The primary objects of interest are partially coherent states that are uniformly "twisted" in space. To analyze these we take the continuum limit, perform an Ott/Antonsen reduction, integrate over the natural frequencies and study the resulting spatio-temporal system on an unbounded domain. We show that these twisted states and their stability can be calculated explicitly. We find that stable twisted states with different wave numbers appear for increasing coupling strength in the well-known Eckhaus scenario. Simulations of finite arrays of oscillators show good agreement with results of the analysis of the infinite system.

Appeared in

  • Chaos, 24 (2014) pp. 023102/1--023102/9.

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