Abstract

A Fokker--Planck-like partial differential equation was recently proposed to represent stochastic neural fields. So far, the PDE has been rigorously derived from a stochastic particle system and its noise-driven spatial-pattern-forming bifurcations have been characterized. However, due to its nonlinear and non-local nature, it is not obvious how to determine the stability of the stationary states for different noise strengths. In this talk, I will present some recent results in this direction. The talk is based on works with Jose A. Carrillo, Helge Holden, and Pierre Roux.