Gradient-Particle Solutions of Fokker-Planck Equations for Noisy Delay Bifurcations

A gradient particle method is used to compute probability densities for processes with delay bifurcations that are sensitive to very small noise. The method is particularly useful for computing the probability density in the transition region, where asymptotic approximations may not be valid. For a one dimensional steady bifurcation problem and a two-dimensional FitzHugh-Nagumo model we solve the Fokker-Planck equation, and compare the results with direct simulations and asymptotic approximations.