Noise-Induced Synchronization and Clustering in Ensembles of Uncoupled Limit-Cycle Oscillators

TL;DR

This paper analyzes how common noise can induce synchronization and clustering in uncoupled limit-cycle oscillators, providing analytical insights into phase behavior under weak noise conditions.

Contribution

It introduces an analytical framework for understanding noise-induced synchronization and clustering in uncoupled oscillators using phase reduction and averaging methods.

Findings

Common noise leads to synchronization and clustering.

Stationary phase difference distribution derived analytically.

Synchronization occurs regardless of initial conditions.

Abstract

We study synchronization properties of general uncoupled limit-cycle oscillators driven by common and independent Gaussian white noises. Using phase reduction and averaging methods, we analytically derive the stationary distribution of the phase difference between oscillators for weak noise intensity. We demonstrate that in addition to synchronization, clustering, or more generally coherence, always results from arbitrary initial conditions, irrespective of the details of the oscillators.