Abstract
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 language | English (US) |
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Article number | 103109 |
Journal | Chaos |
Volume | 28 |
Issue number | 10 |
DOIs | |
State | Published - Oct 1 2018 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics