Phase synchronization between collective rhythms of globally coupled oscillator groups: noiseless non-identical case

TL;DR

This paper analyzes how two groups of non-identical oscillators can synchronize their collective rhythms through global coupling, revealing counterintuitive synchronization behaviors despite microscopic coupling phases.

Contribution

It derives analytical equations for collective oscillations using the Ott-Antonsen ansatz and uncovers novel synchronization phenomena in non-identical oscillator groups.

Findings

Groups can synchronize in anti-phase despite in-phase microscopic coupling.

Groups can synchronize in-phase despite anti-phase microscopic coupling.

Analytical formulas for collective phase coupling functions are provided.

Abstract

Phase synchronization between collective oscillations exhibited by two weakly interacting groups of non-identical phase oscillators with internal and external global sinusoidal coupling of the groups is analyzed theoretically. Coupled amplitude equations describing the collective oscillations of the oscillator groups are obtained by using the Ott-Antonsen ansatz, and then coupled phase equations for the collective oscillations are derived by phase reduction of the amplitude equations. The collective phase coupling function, which determines the dynamics of macroscopic phase differences between the groups, is calculated analytically. It is demonstrated that the groups can exhibit effective anti-phase collective synchronization even if the microscopic external coupling between individual oscillator pairs belonging to different groups is in-phase, and similarly effective in-phase collective synchronization in spite of microscopic anti-phase external coupling between the groups.