Chaos in Kuramoto oscillator networks

TL;DR

This paper demonstrates that simple networks of coupled Kuramoto oscillators can exhibit universal chaotic dynamics, even in minimal configurations, challenging assumptions about their predictable behavior.

Contribution

It proves that chaos can occur in small, simple Kuramoto oscillator networks with generic coupling, extending previous conjectures to finite and minimal systems.

Findings

Chaotic dynamics are universal across network sizes.

Chaos occurs even in networks with just two oscillators per population.

Chaotic mean-field behavior arises with generic coupling schemes.

Abstract

Kuramoto oscillators are widely used to explain collective phenomena in networks of coupled oscillatory units. We show that simple networks of two populations with a generic coupling scheme, where both coupling strengths and phase lags between and within populations are distinct, can exhibit chaotic dynamics as conjectured by Ott and Antonsen [Chaos, 18, 037113 (2008)]. These chaotic mean-field dynamics arise universally across network size, from the continuum limit of infinitely many oscillators down to very small networks with just two oscillators per population. Hence, complicated dynamics are expected even in the simplest description of oscillator networks.