Stochastic resonant media: Signal-to-noise ratio for the activator-inhibitor system through a quasivariational approach

We have made an analytical study of the phenomenon of stochastic resonance in a spatially extended stochastic system of the activator-inhibitor kind. In its bistable regime, through a quasivariational approach we make an approximate evaluation of the nonequilibrium potential for this system. The latter in turn allows us to obtain the probability for the decay of the (extended) metastable states and through it the signal-to-noise ratio within the framework of a two-state description. The analytical results show that this ratio increases with the. activator's diffusivity, whereas it exhibits nonmonotonic behavior against variation of the coupling between both fields.