A stochastic approximation for the finite-size Kuramoto-Sakaguchi model
Abstract
We perform a stochastic model reduction of the Kuramoto-Sakaguchi model for finitely many coupled phase oscillators with phase frustration. Whereas in the thermodynamic limit coupled oscillators exhibit stationary states and a constant order parameter, finite-size networks exhibit persistent temporal fluctuations of the order parameter. These fluctuations are caused by the interaction of the synchronized oscillators with the non-entrained oscillators. We present numerical results suggesting that the collective effect of the non-entrained oscillators on the synchronized cluster can be approximated by a Gaussian process. This allows for an effective closed evolution equation for the synchronized oscillators driven by a Gaussian process which we approximate by a two-dimensional Ornstein-Uhlenbeck process. Our reduction reproduces the stochastic fluctuations of the order parameter and leads to a simple stochastic differential equation for the order parameter.
Cite
@article{arxiv.2310.20048,
title = {A stochastic approximation for the finite-size Kuramoto-Sakaguchi model},
author = {Wenqi Yue and Georg A. Gottwald},
journal= {arXiv preprint arXiv:2310.20048},
year = {2024}
}