Mean-Field Approach to Finite-Size Fluctuations in the Kuramoto-Sakaguchi Model.

Authors

Oleh E Omel'chenko, Georg A Gottwald

Published in

Physical review letters. Volume 136. Issue 24. Pages 247201. Jun 19, 2026.

Abstract

We develop an ab initio approach to describe the statistical behavior of finite-size fluctuations in the deterministic Kuramoto-Sakaguchi model. We obtain explicit expressions for the covariance function of fluctuations of the complex order parameter and determine the variance of its magnitude entirely in terms of the equation parameters. Our results rely on an explicit complex-valued formula for the solution of the Adler equation. We present analytical results for both the sub- and the supercritical case. Moreover, our framework does not require any prior knowledge about the structure of the partially synchronized state. We corroborate our results with numerical simulations of the full Kuramoto-Sakaguchi model. The proposed methodology is sufficiently general such that it can be applied to other interacting particle systems.

PMID:
42412468
Bibliographic data and abstract were imported from PubMed on 07 Jul 2026.

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