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Date
2024-03Type
- Journal Article
ETH Bibliography
yes
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Abstract
The Kuramoto model is a classical mathematical model in the field of nonlinear dynamical systems that describes the evolution of coupled oscillators in a network that may reach a synchronous state. The relationship between the network's topology and whether the oscillators synchronize is a central question in the field of synchronization, and random graphs are often employed as a proxy for complex networks. On the other hand, the random graphs on which the Kuramoto model is rigorously analyzed in the literature are homogeneous models and fail to capture the underlying geometric structure that appears in several examples. In this work, we leverage tools from random matrix theory, random graphs, and mathematical statistics to prove that the Kuramoto model on a random geometric graph on the sphere synchronizes with probability tending to one as the number of nodes tends to infinity. To the best of our knowledge, this is the first rigorous result for the Kuramoto model on random geometric graphs. Show more
Publication status
publishedExternal links
Journal / series
SIAM Journal on Applied Dynamical SystemsVolume
Pages / Article No.
Publisher
SIAMSubject
Kuramoto; complex networks; dynamical systems; random graphsRelated publications and datasets
Is new version of: https://doi.org/10.3929/ethz-b-000655257
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ETH Bibliography
yes
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