Synchronization of coupled active rotators by common noise

TL;DR

This paper investigates how common noise influences the synchronization of coupled active rotators, revealing complex behaviors like phase locking, anti-entrainment, and a power-law relationship in frequency repulsion.

Contribution

The authors develop an analytical method using angle-action variables and averaging to analyze synchronization phenomena in coupled active rotators under common noise.

Findings

Common noise always promotes synchrony.

Transition from full to partial synchrony at a critical repulsive coupling.

Observation of phase locking and anti-entrainment at moderate repulsive coupling.

Abstract

We study the effect of common noise on coupled active rotators. While such a noise always facilitates synchrony, coupling may be attractive or repulsing. We develop an analytical approach based on a transformation to approximate angle-action variables and averaging over fast rotations. For identical rotators, we describe a transition from full to partial synchrony at a critical value of repulsive coupling. For nonidentical rotators, the most nontrivial effect occurs at moderate repulsive coupling, where a juxtaposition of phase locking with frequency repulsion (anti-entrainment) is observed. We show that the frequency repulsion obeys a nontrivial power law.