Inter-community resonances in multifrequency ensembles of coupled oscillators

TL;DR

This paper extends the Kuramoto model to multifrequency communities, revealing how cross-coupling can induce synchronization or chaos, with complex multi-branch entrainment phenomena.

Contribution

It introduces a generalized model for multifrequency oscillator communities and analyzes the effects of cross-frequency coupling on synchronization and chaos.

Findings

Cross-coupling can promote synchrony even in asynchronous ensembles.

Transition to synchrony involves multiple distinct solutions due to multi-branch entrainment.

Cross-frequency coupling can also destroy phase-locking, leading to chaotic dynamics.

Abstract

We generalize the Kuramoto model of globally coupled oscillators to multifrequency communities. A situation when mean frequencies of two subpopulations are close to resonance 2:1 is considered in detail. We derive uniformly rotating solutions describing synchronization inside communities and between them. Remarkably, cross-coupling between the frequency scales can promote synchrony even when ensembles are separately asynchronous. We also show that the transition to synchrony due to the cross-coupling is accompanied by a huge multiplicity of distinct synchronous solutions what is directly related to a multi-branch entrainment. On the other hand, for synchronous populations, the cross-frequency coupling can destroy a phase-locking and lead to chaos of mean fields.