Kuramoto model with coupling through an external medium

TL;DR

This paper introduces a generalized Kuramoto model where oscillators communicate via an external medium, revealing new phenomena like bistability and unique synchronization behaviors, and relates it to other Kuramoto variations.

Contribution

The paper presents a novel extension of the Kuramoto model incorporating external medium coupling, uncovering new synchronization phenomena and connecting to existing models.

Findings

Discovery of bistability between synchronization and incoherence

Identification of a new form of synchronization with medium oscillations

Relation to other Kuramoto model variants and the Millennium Bridge problem

Abstract

Synchronization of coupled oscillators is often described using the Kuramoto model. Here we study a generalization of the Kuramoto model where oscillators communicate with each other through an external medium. This generalized model exhibits interesting new phenomena such as bistability between synchronization and incoherence and a qualitatively new form of synchronization where the external medium exhibits small-amplitude oscillations. We conclude by discussing the relationship of the model to other variations of the Kuramoto model including the Kuramoto model with a bimodal frequency distribution and the Millennium Bridge problem.