CUED Publications database

Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere

Markdahl, J and Proverbio, D and Mi, L and Goncalves, J (2021) Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere. Communications Physics, 4.

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Abstract

From the flashing of fireflies to autonomous robot swarms, synchronization phenomena are ubiquitous in nature and technology. They are commonly described by the Kuramoto model that, in this paper, we generalise to networks over n-dimensional spheres. We show that, for almost all initial conditions, the sphere model converges to a set with small diameter if the model parameters satisfy a given bound. Moreover, for even n, a special case of the generalized model can achieve phase synchronization with nonidentical frequency parameters. These results contrast with the standard n = 1 Kuramoto model, which is multistable (i.e., has multiple equilibria), and converges to phase synchronization only if the frequency parameters are identical. Hence, this paper shows that the generalized network Kuramoto models for n ≥ 2 displays more coherent and predictable behavior than the standard n = 1 model, a desirable property both in flocks of animals and for robot control.

Item Type: Article
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 27 Aug 2021 22:49
Last Modified: 02 Sep 2021 05:26
DOI: 10.1038/s42005-021-00689-y