2002 -06 -05
10 :15 at ML J 21

Multicomponent systems described by nonlinear Fokker-Planck equations

Till D. Frank

Institute for Theoretical Physics, University of Muenster, Germany

Mesoscopic stochastic descriptions of many particle systems have frequently been used in the context of mean field nonlinear Fokker-Planck equations and nonlinear diffusion equations. We discuss a recent attempt to obtain a unified description for stochastic relaxation processes that are characterized by mean field interactions, on the one hand, and nonlinear diffusion terms, on the other hand. We show that in general there are multiple stationary distributions and that stationary distributions can differ from Boltzmann distributions. As for the transient case, we illustrate that transient solutions converge to stationary ones. Finally, we exemplify that bifurcation theory can be carried out for nonlinear Fokker-Planck equations using a model of coupled neural oscillators.