Phase synchronization between collective rhythms of globally coupled oscillator groups: noisy identical case

TL;DR

This paper develops a theoretical framework to analyze how groups of noisy, identical oscillators synchronize their collective rhythms, revealing that macroscopic synchronization can differ from microscopic coupling.

Contribution

It derives coupled phase equations for collective rhythms from microscopic Langevin equations, showing how macroscopic synchronization types can differ from microscopic interactions.

Findings

Macroscopic rhythms can exhibit anti-phase synchronization despite in-phase microscopic coupling.

Analytical expressions for collective phase coupling near oscillation onset.

Theoretical prediction of synchronization behavior in noisy oscillator groups.

Abstract

We theoretically investigate collective phase synchronization between interacting groups of globally coupled noisy identical phase oscillators exhibiting macroscopic rhythms. Using the phase reduction method, we derive coupled collective phase equations describing the macroscopic rhythms of the groups from microscopic Langevin phase equations of the individual oscillators via nonlinear Fokker-Planck equations. For sinusoidal microscopic coupling, we determine the type of the collective phase coupling function, i.e., whether the groups exhibit in-phase or anti-phase synchronization. We show that the macroscopic rhythms can exhibit effective anti-phase synchronization even if the microscopic phase coupling between the groups is in-phase, and vice versa. Moreover, near the onset of collective oscillations, we analytically obtain the collective phase coupling function using center-manifold and phase reductions of the nonlinear Fokker-Planck equations.