Effects of non-resonant interaction in ensembles of phase oscillators

TL;DR

This paper investigates the dynamics of multiple groups of non-resonantly interacting oscillators, revealing regimes like co-synchrony, heteroclinic cycles, and chaos through a reduced order parameter model.

Contribution

It introduces a novel analysis of non-resonant oscillator groups using the Ott-Antonsen ansatz, extending understanding of complex collective behaviors.

Findings

Identification of co-synchrony regimes

Existence of heteroclinic cycles in large groups

Observation of chaotic oscillations in order parameters

Abstract

We consider general properties of groups of interacting oscillators, for which the natural frequencies are not in resonance. Such groups interact via non-oscillating collective variables like the amplitudes of the order parameters defined for each group. We treat the phase dynamics of the groups using the Ott-Antonsen ansatz and reduce it to a system of coupled equations for the order parameters. We describe different regimes of co-synchrony in the groups. For a large number of groups, heteroclinic cycles, corresponding to a sequental synchronous activity of groups, and chaotic states, where the order parameters oscillate irregularly, are possible.