The Kuramoto model on dynamic random graphs

Pablo Groisman; Ruojun Huang; Hernan Vivas

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arXiv · 2206.02642

The Kuramoto model on dynamic random graphs

Pablo Groisman·Ruojun Huang·Hernan Vivas

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Abstract

We propose a Kuramoto model of coupled oscillators on a time-varying graph, whose dynamics is dictated by a Markov process in the space of graphs. The simplest representative is considering a base graph and then the subgraph determined by $N$ independent random walks on the underlying graph. We prove a synchronization result for solutions starting from a phase-cohesive set independent of the speed of the random walkers, an averaging principle and a global synchronization result with high probability for sufficiently fast processes. We also consider Kuramoto oscillators in a dynamical version of the Random Conductance Model.

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BibTeX RIS

Pablo Groisman, Ruojun Huang, Hernan Vivas. 2022-06-06. The Kuramoto model on dynamic random graphs. https://arxiv.org/abs/2206.02642

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