Configurational stability for the Kuramoto-Sakaguchi model

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The Kuramoto-Sakaguchi model is a generalization of the well-known Kuramoto model that adds a phase-lag paramater or "frustration" to a network of phase-coupled oscillators. The Kuramoto model is a flow of gradient type, but adding a phase-lag breaks the gradient structure, significantly complicating the analysis of the model. We present several results determining the stability of phase-locked configurations: the first of these gives a sufficient condition for stability, and the second a sufficient condition for instability. In fact, the instability criterion gives a count, modulo 2, of the dimension of the unstable manifold to a fixed point and having an odd count is a sufficient condition for instability of the fixed point. We also present numerical results for both small (N≤10) and large (N=50) collections of Kuramoto-Sakaguchi oscillators.

Original languageEnglish (US)
Article number103109
Issue number10
StatePublished - Oct 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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