Kuramoto model with coupling through an external medium

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.

9 pages, 3 figures

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Cited by in corpus (5)

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• Quasi phase reduction of all-to-all strongly coupled $\lambda -\omega$ oscillators near incoherent states
• Spatio-temporal dynamics of Kuramoto-Sakaguchi model with time dependent connectivity
• Diversity of dynamical behaviors due to initial conditions: exact results with extended Ott--Antonsen ansatz for identical Kuramoto--Sakaguchi phase oscillators