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

Author:

Wenqi Yue, Georg A. Gottwald

Keyword:

Nonlinear Sciences, Adaptation and Self-Organizing Systems, Adaptation and Self-Organizing Systems (nlin.AO), Dynamical Systems (math.DS)

journal:

date:

2023-10-29 16:00:00

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 show 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 equations for the synchronized oscillators driven 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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