Chaos in Symmetric Phase Oscillator Networks

TL;DR

This paper demonstrates that symmetric networks of identical phase oscillators can exhibit chaotic dynamics and fluctuations in the order parameter, challenging the notion that inhomogeneities are necessary for chaos.

Contribution

It reveals that chaos can arise purely from nonlinear phase interactions in symmetric oscillator networks, without inhomogeneities or amplitude variations.

Findings

Symmetric identical oscillators can produce chaotic order parameters.

Chaos does not require inhomogeneities or amplitude variations.

Nonlinear phase interactions induce instabilities leading to chaos.

Abstract

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos, i.e., nonlinear interactions of phases give rise to the necessary instabilities.