Transition rates in a bistable system driven by external dichotomous noise

A study of dichotomous noise-induced transitions is presented for a simple one-dimensional system exhibiting deterministic bistability between two steady states. A phenomenological rate law for the kinetics of such transitions is derived and the corresponding rate coefficient is evaluated. Critical slowing down for such transitions is shown to be possible and an asymptotic scaling form for the rate coefficient is derived. Finally, memory effects and the breakdown of the phenomenological rate law due to the magnitude of the noise correlation time are discussed.