Dynamics of multifrequency oscillator communities

TL;DR

This paper extends the Kuramoto model to multiple oscillator communities with different natural frequencies, analyzing how their interactions can lead to synchronization, partial asynchrony, or chaos.

Contribution

It derives general equations for resonances between communities and analyzes the dynamics of three interacting groups, revealing conditions for various synchronization states.

Findings

Interaction can promote or suppress synchrony.

Multiple interaction regimes including chaos.

Conditions for resonance-induced synchronization.

Abstract

We consider a generalization of the Kuramoto model of coupled oscillators to the situation where communities of oscillators having essentially different natural frequencies interact. General equations describing possible resonances between the communities' frequencies are derived. The mostly simple situation of three resonantly interacting groups is analyzed in details. We find conditions for the mutual coupling to promote or suppress synchrony in individual populations, and present examples where interaction between communities leads to their synchrony, or to a partially asynchronous state, or to a chaotic dynamics of order parameters.