Applied Mathematics Colloquia with Mete Soner: Synchronization in a Kuramoto Mean Field Game

Speaker: Mete Soner, Princeton University

Title: Synchronization in a Kuramoto Mean Field Game

Abstract: 

Originally motivated by systems of chemical  and biological oscillators, the classical Kuramoto model has found an amazing range of applications from neuroscience to Josephson junctions in superconductors, and  has become a  key mathematical model to describe self organization in complex systems. These autonomous oscillators are coupled through a nonlinear interaction term which plays a central role in the long term behavior  of the system. While the system is unsynchronized when this term is not sufficiently strong, fascinatingly, they exhibit an abrupt transition to a full synchronization above a critical value of the interaction parameter.  We explore this system in the mean field formalism.  We treat the system of oscillators as an infinite particle system, but instead of positing the dynamics of the particles, we let the individual particles determine endogenously their behaviors by minimizing a cost functional and eventually, settling in a Nash equilibrium.  The mean field game also exhibits a bifurcation from unsynhcronization to self-organization.  This approach has found interesting applications including circadian rhythms and jet-lag recovery.  This is joint work with Rene Carmona and Quentin Cormier of Princeton University.

 

Applied Mathematics Colloquia