Stochastic resonant media: Effect of local and nonlocal coupling in reaction-diffusion models

We study the phenomenon of stochastic resonance in spatially extended systems or stochastic resonant media. Two reaction-diffusion models are analyzed (with one and two components, respectively), both with a known form of the nonequilibrium potential that is exploited to obtain first the probability for the decay of the metastable extended states and second expressions for the correlation function and for the signal-to-noise ratio, within the framework of a two-state description. The analytical results show that this ratio increases with bath local and nonlocal coupling parameters.