Calculus of Variations and Geometric Measure Theory

A. Cesaroni - M. Cirant

Stationary equilibria and their stability in a Kuramoto MFG with strong interaction

created by cesaroni on 19 Jul 2023
modified on 06 Feb 2024


Published Paper

Inserted: 19 jul 2023
Last Updated: 6 feb 2024

Journal: Comm. Partial Differential Equations
Year: 2024

ArXiv: 2307.09305 PDF


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.