Mathematics Colloquium
Synchronization in the Kuramoto Mean Field Game and an Application to Jet Lag Recovery
Speaker: Rene Carmona, Princeton
Location: Warren Weaver Hall 1302
Date: Monday, November 21, 2022, 3:45 p.m.
Synopsis:
We study the classical Kuramoto model as an infinite horizon mean field game. The system is shown to exhibit both incoherence and synchronization:
1) Incoherence when the interaction parameter is below a sharp critical value follows the stability of the uniform distribution.
2) Above the critical value, the game bifurcates and develops self-organizing time homogeneous Nash equilibria. As interactions strengthen, these stationary solutions become fully synchronized. Results are proved by a patchwork of techniques from nonlinear partial differential equations and stochastic optimal control. If time permits, the inclusion of a forcing term and an application to jet lag recovery will be discussed.
The talk will draw from an older paper with C. Graves and a recent work with M. Soner and Q. Cormier.