Stationary equilibria and their stability in a Kuramoto MFG with strong interaction
Analysis of PDEs
2023-07-19 v1
Abstract
Recently, R. Carmona, Q. Cormier, and M. Soner proposed a Mean Field Game (MFG) version of the classical Kuramoto model, which describes synchronization phenomena in a large population of rational interacting oscillators. The MFG model exhibits several stationary equilibria, but the characterization of these equilibria and their ability to capture dynamic equilibria in long time remains largely open. In this paper, we demonstrate that, up to a phase translation, there are only two possible stationary equilibria: the incoherent equilibrium and the self-organizing equilibrium, given that the interaction parameter is sufficiently large. Furthermore, we present some local stability properties of the self-organizing equilibrium.
Keywords
Cite
@article{arxiv.2307.09305,
title = {Stationary equilibria and their stability in a Kuramoto MFG with strong interaction},
author = {Annalisa Cesaroni and Marco Cirant},
journal= {arXiv preprint arXiv:2307.09305},
year = {2023}
}