Stochastic resonance in an activator–inhibitor system through adiabatic and quasi-variational approaches

We study the phenomenon of stochastic resonance in a spatially extended system. An activator–inhibitor reaction–diffusion model is analyzed through two different approximations: an adiabatic one leading to a known form of the Graham’s nonequilibrium potential, and a quasi-variational approach that allows to obtain an approximated form of Graham’s potential for a different parameter region. Those potentials have been exploited to obtain, firstly the probability for the decay of the metastable extended states, and secondly expressions for the correlation function and for the signal-to-noise ratio, within the framework of a two state description. The analytical results show how this ratio depends on both local and nonlocal coupling parameters.