WIAS Preprint No. 1791, (2013)

Bifurcations in the Sakaguchi--Kuramoto model


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

2010 Mathematics Subject Classification

  • 34C15 37N20 37N25

2008 Physics and Astronomy Classification Scheme

  • 05.45.Xt 89.79.Kd


  • synchronization, coupled oscillators, Sakaguchi-Kuramoto model, Ott-Antonsen reduction


We analyze the Sakaguchi-Kuramoto model of coupled phase oscillators in a continuum limit given by a frequency dependent version of the Ott-Antonsen system. Based on a self-consistency equation, we provide a detailed analysis of partially synchronized states, their bifurcation from the completely incoherent state and their stability properties. We use this method to analyze the bifurcations for various types of frequency distributions and explain the appearance of non-universal synchronization transitions.

Appeared in

  • Phys. D, 263 (2013) pp. 74--85.

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