Collective Phase Chaos in the Dynamics of Interacting Oscillator Ensembles

TL;DR

This paper investigates chaotic collective dynamics in two coupled oscillator ensembles with alternating synchronization, revealing that their phases follow an expanding circle map similar to the Bernoulli map, supported by Lyapunov analysis.

Contribution

It demonstrates the emergence of collective chaos governed by an expanding circle map in coupled oscillator ensembles with alternating synchronization.

Findings

Collective phases follow an expanding circle map similar to Bernoulli map.

Chaotic behavior arises during alternating synchronization transitions.

Finite-size effects influence the observed dynamics.

Abstract

We study chaotic behavior of order parameters in two coupled ensembles of self-sustained oscillators. Coupling within each of these ensembles is switched on and off alternately, while the mutual interaction between these two subsystems is arranged through quadratic nonlinear coupling. We show numerically that in the course of alternating Kuramoto transitions to synchrony and back to asynchrony, the exchange of excitations between two subpopulations proceeds in such a way that their collective phases are governed by an expanding circle map similar to the Bernoulli map. We perform the Lyapunov analysis of the dynamics and discuss finite-size effects.