Chaos in generically coupled phase oscillator networks with nonpairwise interactions

TL;DR

This paper demonstrates that nonpairwise interactions in coupled phase oscillator networks can induce complex dynamics, including chaos, even in minimal four-oscillator systems, extending understanding beyond traditional pairwise models.

Contribution

It reveals that nonpairwise coupling introduces complex behaviors like chaos in symmetric oscillator networks, which was not observed in purely pairwise models.

Findings

Chaos can emerge in four-oscillator systems due to nonpairwise interactions.

Nonpairwise interactions lead to richer dynamics than pairwise models.

Complex bifurcations occur in minimal oscillator networks with nonpairwise coupling.

Abstract

The Kuramoto-Sakaguchi system of coupled phase oscillators, where interaction between oscillators is determined by a single harmonic of phase differences of pairs of oscillators, has very simple emergent dynamics in the case of identical oscillators that are globally coupled: there is a variational structure that means the only attractors are full synchrony (in-phase) or splay phase (rotating wave/full asynchrony) oscillations and the bifurcation between these states is highly degenerate. Here we show that nonpairwise coupling - including three and four-way interactions of the oscillator phases - that appears generically at the next order in normal-form based calculations, can give rise to complex emergent dynamics in symmetric phase oscillator networks. In particular, we show that chaos can appear in the smallest possible dimension of four coupled phase oscillators for a range of parameter values.