STOCHASTIC RESONANCE IN AN ACTIVATOR-INHIBITOR SYSTEM THROUGH ADIABATIC AND QUASI-VARIATIONAL APPROACHES

We study the phenomenon of stochastic resonance in a spatially extende d system. An activator-inhibitor reaction-diffusion model is analyzed through two different approximations: an adiabatic one leading to a kn own form of the Graham's nonequilibrium potential, and a quasi-variati onal approach that allows to obtain an approximated form of Graham's p otential for a different parameter region. Those potentials have been exploited to obtain, firstly the probability for the decay of the meta stable extended states, and secondly expressions for the correlation f unction and for the signal-to-noise ratio, within the framework of a t wo state description. The analytical results shaw how this ratio depen ds on both local and nonlocal coupling parameters. (C) 1998 Elsevier S cience B.V. All rights reserved.