Generating macroscopic chaos in a network of globally coupled phase oscillators

TL;DR

This paper demonstrates that a network of globally coupled phase oscillators with bimodal frequency distribution can exhibit macroscopic chaos when the coupling strength varies periodically, revealing complex bifurcation structures.

Contribution

It introduces the phenomenon of macroscopic chaos in a bimodal Kuramoto model with time-varying coupling, extending understanding of collective dynamics in oscillator networks.

Findings

Identification of period-doubling cascades to chaos

Observation of attractor crises and horseshoe dynamics

Mechanistic explanation based on bifurcation analysis

Abstract

We consider an infinite network of globally-coupled phase oscillators in which the natural frequencies of the oscillators are drawn from a symmetric bimodal distribution. We demonstrate that macroscopic chaos can occur in this system when the coupling strength varies periodically in time. We identify period-doubling cascades to chaos, attractor crises, and horseshoe dynamics for the macroscopic mean field. Based on recent work that clarified the bifurcation structure of the static bimodal Kuramoto system, we qualitatively describe the mechanism for the generation of such complicated behavior in the time varying case.