Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations

Eric Luçon (1, 2) , Christophe Poquet (3)

1 FP2M - Fédération Parisienne de Modélisation Mathématique
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 PSPM - Probabilités, statistique, physique mathématique

We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within 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.

Domaines: Probabilités [math.PR]

Eric Luçon, Christophe Poquet. Existence, stability and regularity of periodic solutions for nonlinear Fokker-Planck equations. Journal of Dynamics and Differential Equations, 2022, ⟨10.1007/s10884-022-10148-z⟩. ⟨hal-03280094⟩