Robust chaos in a totally symmetric network of four phase oscillators

TL;DR

This paper identifies conditions under which a symmetric network of four identical oscillators exhibits robust chaotic attractors, including Lorenz-like structures, and verifies their stability through theoretical and numerical methods.

Contribution

It introduces specific coupling conditions that produce robust chaos in a symmetric oscillator network, extending understanding of chaotic attractors in such systems.

Findings

Chaotic attractors emerge near the triple instability threshold.

Chaotic dynamics are verified to be pseudohyperbolic and robust.

Robust chaos can be inherited by larger networks with similar attractors.

Abstract

We provide conditions on the coupling function such that a system of 4 globally coupled identical oscillators has chaotic attractors, a pair of Lorenz attractors or a 4-winged analogue of the Lorenz attractor. The attractors emerge near the triple instability threshold of the splay-phase synchronization state of the oscillators. We provide theoretical arguments and verify numerically, based on the pseudohyperbolicity test, that the chaotic dynamics are robust with respect to small, e.g. time-dependent, perturbations of the system. The robust chaoticity should also be inherited by any network of weakly interacting systems with such attractors.