Configurational stability for the Kuramoto-Sakaguchi model
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.
Cite
@article{arxiv.1803.07962,
title = {Configurational stability for the Kuramoto-Sakaguchi model},
author = {Jared Bronski and Thomas Carty and Lee DeVille},
journal= {arXiv preprint arXiv:1803.07962},
year = {2018}
}