Phase Reduction and Synchronization of Coupled Noisy Oscillators

TL;DR

This paper investigates synchronization in noisy oscillator networks, deriving conditions for synchronization using phase response curves and reduced stochastic models, applicable to various systems.

Contribution

It introduces a reduced stochastic phase model for noisy oscillators and provides new synchronization conditions based on phase response curves.

Findings

Derived a reduced phase equation for noisy oscillators.

Established synchronization criteria using PRCs.

Validated results on specific oscillator models.

Abstract

We study the synchronization behavior of a noisy network in which each system is driven by two sources of state-dependent noise: (1) an intrinsic noise which is common among all systems and can be generated by the environment or any internal fluctuations, and (2) a coupling noise which is generated by interactions with other systems. After providing sufficient conditions that foster synchronization in networks of general noisy systems, we focus on weakly coupled networks of noisy oscillators and, using the first- and second-order phase response curves (PRCs), we derive a reduced order stochastic differential equation to describe the corresponding phase evolutions. Finally, we derive synchronization conditions based on the PRCs and illustrate the theoretical results on a couple of models.