Heteroclinic cycles and chaos in a system of four identical phase oscillators with global biharmonic coupling

TL;DR

This paper investigates a minimal system of four identical phase oscillators with biharmonic coupling, demonstrating the existence of chaos through heteroclinic cycles and symmetry analysis, which was previously unconfirmed.

Contribution

It introduces a novel approach to identify heteroclinic cycles and provides the first numerical evidence of chaos in this minimal oscillator system.

Findings

Existence of heteroclinic cycles in the system

Numerical evidence of chaotic dynamics

Symmetry-driven mechanisms for chaos emergence

Abstract

We study a system of four identical globally coupled phase oscillators with biharmonic coupling function. Its dimension and the type of coupling make it the minimal system of Kuramoto-type (both in the sense of the phase space's dimension and the number of harmonics) that supports chaotic dynamics. However, to the best of our knowledge, there is still no numerical evidence for the existence of chaos in this system. The dynamics of such systems is tightly connected with the action of the symmetry group on its phase space. The presence of symmetries might lead to an emergence of chaos due to scenarios involving specific heteroclinic cycles. We suggest an approach for searching such heteroclinic cycles and showcase first examples of chaos in this system found by using this approach.