Liapunov functionals and large-time-asymptotics of mean-field nonlinear Fokker-Planck equations

Abstract

Large-time asymptotics of the solutions of time-dependent mean-field nonlinear Fokker-Planck systems are analyzed by exploiting the properties of Liapunov functionals (relative entropies). We first discuss the scalar Desai-Zwanzig model and then generalize the techniques to a general class of mean-field oscillator equations.

Systems of this type are relevant in the modeling of synchronization of a large population of coupled nonlinear oscillators in the presence of external or thermal white noise.