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arXiv · 1803.07962

Configurational stability for the Kuramoto-Sakaguchi model

Jared Bronski·Thomas Carty·Lee DeVille
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Abstract

The Kuramoto--Sakaguchi model is a modification 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 and large collections of Kuramoto--Sakaguchi oscillators.

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Jared Bronski, Thomas Carty, Lee DeVille. 2018-03-21. Configurational stability for the Kuramoto-Sakaguchi model. https://doi.org/10.1063/1.5029397

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