Coupled networks and networks with bimodal frequency distributions are equivalent

TL;DR

This paper demonstrates that coupled networks with unimodal frequency distributions can exhibit synchronization behaviors similar to single populations with bimodal distributions, using the Ott-Antonsen ansatz for analysis.

Contribution

It establishes the equivalence in stability, dynamics, and bifurcations between coupled unimodal populations and bimodal frequency distributions, extending understanding of synchronization patterns.

Findings

Coupled unimodal populations can mimic bimodal frequency distribution behaviors.

The Ott-Antonsen ansatz is used to prove the equivalence in stability and bifurcations.

Generalization to multiple subpopulations or multimodal distributions is not straightforward.

Abstract

Populations of oscillators can display a variety of synchronization patterns depending on the oscillators' intrinsic coupling and the coupling between them. We consider two coupled, symmetric (sub)populations with unimodal frequency distributions and show that the resulting synchronization patterns may resemble those of a single population with bimodally distributed frequencies. Our proof of the equivalence of their stability, dynamics, and bifurcations, is based on an Ott-Antonsen ansatz. The generalization to networks consisting of multiple (sub)populations vis-\`a-vis networks with multimodal frequency distributions, however, appears impossible.