  In this paper we consider systems of weakly interacting particles driven by
colored noise in a bistable potential, and we study the effect of the
correlation time of the noise on the bifurcation diagram for the equilibrium
states. We accomplish this by solving the corresponding McKean-Vlasov equation
using a Hermite spectral method, and we verify our findings using Monte Carlo
simulations of the particle system. We consider both Gaussian and non-Gaussian
noise processes, and for each model of the noise we also study the behavior of
the system in the small correlation time regime using perturbation theory. The
spectral method that we develop in this paper can be used for solving linear
and nonlinear, local and nonlocal (mean-field) Fokker-Planck equations, without
requiring that they have a gradient structure.
