Colored Noise in Dynamical Systems

We consider the problem of escape of a particle activated by small amplitude Gaussian colored noise, from a potential well. We consider various ranges of the parameters representing the bandwidth of the noise, its spectral height, and the dissipation coefficient. We employ singular perturbation methods to derive explicit analytical approximations for the stationary density of fluctuations about the deterministically meta-stable state at the bottom of the well, and for the mean first passage time to overcome the potential barrier and escape the well. The latter leads to a formula for the escape (activation) rate. Among other results we find that the mean first passage time is exponentially larger than in the white noise case.