Interplay between couplings and common noise in phase synchronization: disagreement between global analysis and local stability characterization

TL;DR

This paper analyzes how coupling strength and common noise influence phase synchronization in coupled oscillators, revealing complex interactions where noise can both hinder and promote synchronization depending on the regime, and emphasizing the limitations of local stability measures.

Contribution

It provides a global analytical study of synchronization under combined coupling and noise, highlighting the disagreement with local stability analysis and identifying conditions where noise enhances synchronization.

Findings

Strong coupling favors synchronization when noise is weak.

High noise levels can induce synchronization in weakly coupled oscillators.

Synchronization is a global property not accurately captured by local stability measures.

Abstract

We consider two coupled phase oscillators in the presence of proportional ("common") and independent white noises. The global synchronization properties of the system are analytically studied via the Fokker-Planck equation. When the "effective coupling" is big compared to the common noises, the former favors and the latter hinder synchronization. On the contrary, when the coupling is small compared to the proportional noises, we find that the latter induce synchronization, optimally when their intensities are big and in the n:m synchronization ratio. Furthermore, in such case a small value of the coupling is better for synchronization. Finally, we show that synchronization, which is a global property, must not be studied via local stability such as with Lyapunov exponents.