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On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph

Verwoerd, Mark and Mason, Oliver (2009) On computing the critical coupling coefficient for the Kuramoto model on a complete bipartite graph. SIAM Journal on Applied Dynamical Systems, 8 (1). pp. 417-453. ISSN 1536-0040

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Abstract

We extend recent results [50] on the existence of global phase-locked states (GPLS) in the Kuramoto model on a complete graph to the case of a complete bipartite graph. In particular, we prove that, for the Kuramoto model on a complete bipartite graph, the value of the critical coupling co- efficient can be determined by solving a system of two nonlinear equations that do not depend on the coupling coefficient. We show that the said system of equations can be solved using an efficient algorithm described in the paper.

Item Type: Article
Keywords: coupling coefficient; Kuramoto model; coupled oscillators; synchronization; phase-locking; bipartite graph;
Subjects: Science & Engineering > Hamilton Institute
Item ID: 2137
Depositing User: Oliver Mason
Date Deposited: 29 Sep 2010 15:26
Journal or Publication Title: SIAM Journal on Applied Dynamical Systems
Publisher: SIAM - Society for Industrial and Applied Mathematics
Refereed: Yes
URI:

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