Nucleation of Waves in Excitable Media by Noise

We are interested in reaction-diffusion equations that model excitable media under the influence of an additive noise. In many models of this type, the homogeneous zero state is stable and interesting dynamics is observed only for certain initial data. In the presence of noise, the excitable media is stimulated and the noise may be sufficiently large to nucleate wave forms. In computations, we see for small noise that only target waves are nucleated when the time scales for excitation and inhibition are sufficiently separated. We provide a theorem that supports this observation.