A stochastic approximation for the finite-size Kuramoto-Sakaguchi model

Wenqi Yue; Georg A. Gottwald

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arXiv · 2310.20048

A stochastic approximation for the finite-size Kuramoto-Sakaguchi model

Wenqi Yue·Georg A. Gottwald

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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.

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Wenqi Yue, Georg A. Gottwald. 2023-10-30. A stochastic approximation for the finite-size Kuramoto-Sakaguchi model. https://arxiv.org/abs/2310.20048

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