Existence, Stability and Regularity of Periodic Solutions for Nonlinear Fokker–Planck Equations

Abstract

We consider a class of nonlinear Fokker–Planck equations describing the dynamics of an infinite population of units with mean-field interaction. Relying on a slow–fast viewpoint and on the theory of approximately invariant manifolds we obtain the existence of a stable periodic solution for the PDE, consisting of probability measures. Moreover we establish the existence of a smooth isochron map in the neighborhood of this periodic solution.