Synchronization in a Kuramoto mean field game model
par
M.Quentin Cormier(Inria Saclay)
→
Europe/Paris
Fokko du Cloux (ICJ, Bâtiment Braconnier)
Description
We study a mean field game version of the Kuramoto model.
The classical Kuramoto model is used to study the synchronization of coupled oscillators.
In this mean field game version, each oscillator controls its phase and minimizes a cost posed on an infinite time horizon.
We are interested in the stationary solutions and their stability. We show the existence of a phase transition.
Below a certain critical parameter, we prove that the agents desynchronized: the distribution of the agents converges, in long time, to the uniform measure.
Above this critical parameter, the game bifurcates and we show the existence of self-organized solutions, corresponding to non-trivial time homogeneous Nash equilibria.
This work is done in collaboration with René Carmona and Mete Soner.
