Frequency assortativity can induce chaos in oscillator networks

TL;DR

This paper demonstrates that frequency assortativity in networks of coupled oscillators can lead to chaotic macroscopic behavior, analyzed through a low-dimensional mean-field model and chaos indicators.

Contribution

It introduces a mean-field and dimension reduction approach to show how frequency assortativity induces chaos in oscillator networks.

Findings

Frequency assortativity can induce chaos in oscillator networks.

Chaos arises from the formation of synchronized oscillator groups.

The reduced model accurately characterizes chaotic dynamics.

Abstract

We investigate the effect of preferentially connecting oscillators with similar frequency to each other in networks of coupled phase oscillators (i.e., frequency assortativity). Using the network Kuramoto model as an example, we find that frequency assortativity can induce chaos in the macroscopic dynamics. By applying a mean-field approximation in combination with the dimension reduction method of Ott and Antonsen, we show that the dynamics can be described by a low dimensional system of equations. We use the reduced system to characterize the macroscopic chaos using Lyapunov exponents, bifurcation diagrams, and time-delay embeddings. Finally, we show that the emergence of chaos stems from the formation of multiple groups of synchronized oscillators, i.e., meta-oscillators.