Irregular collective dynamics in a Kuramoto-Daido system

TL;DR

This paper investigates complex collective behaviors, including long-lasting chaos, in a mean-field model of phase oscillators with multi-harmonic coupling, using numerical simulations and stability analysis.

Contribution

It introduces a detailed analysis of chaotic collective dynamics in a Kuramoto-Daido system with three-harmonic coupling functions, highlighting long-lasting chaos in the thermodynamic limit.

Findings

Evidence of persistent chaotic collective behavior

Identification of the maximum Lyapunov exponent indicating chaos

Analysis of invariant measure structure through entropy

Abstract

We analyse the collective behavior of a mean-field model of phase-oscillators of Kuramoto-Daido type coupled through pairwise interactions which depend on phase differences: the coupling function is composed of three harmonics. We provide convincing evidence of a transient but long-lasting chaotic collective chaos, which persists in the thermodynamic limit. The regime is analysed with the help of clever direct numerical simulations, by determining the maximum Lyapunov exponent and assessing the transversal stability to the self-consistent mean field. The structure of the invariant measure is finally described in terms of a resolution-dependent entropy.