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Expander graphs are globally synchronizing
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AI
DOI：10.1016/j.aim.2025.110773.png)
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Abstract
En 中文
The Kuramoto model is fundamental to the study of synchronization. It consists of a collection of oscillators with interactions given by a network, which we identify respectively with vertices and edges of a graph. In this paper, we show that a graph with sufficient expansion must be globally synchronizing, meaning that a homogeneous Kuramoto model of identical oscillators on such a graph will converge to the fully synchronized state with all the oscillators having the same phase, for every initial state up to a set of measure zero. In particular, we show that for any epsilon > 0 and p >= (1 + epsilon)(log n)/n, the homogeneous Kuramoto model on the Erd & odblac;s-R & eacute;nyi random graph G(n, p) is globally synchronizing with probability tending to one as n goes to infinity. This improves on a previous result of Kassabov, Strogatz, and Townsend and solves a conjecture of Ling, Xu, and Bandeira. We also show that the Kuramoto model is globally synchronizing on any d-regular Ramanujan graph, and on typical d-regular graphs, for d >= 600. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keywords:
Synchronization
Kuramoto model
Expander graphs
Random graphs
Journal
A
IF:
1.5
Papers:
329
Citations:
0
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