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Aspects of stochastic resonance in reaction-diffusion systems: The nonequilibrium-potential approach

We analyze several aspects of the phenomenon of stochastic resonance in reaction-diffusion systems, exploiting the nonequilibrium potential's framework. The generalization of this formalism (sketched in the appendix) to extended systems is first carried out in the context of a simplified scalar model, for which stationary patterns can be found analytically. We first show how system-size stochastic resonance arises naturally in this framework, and then how the phenomenon of array-enhanced stochastic resonance can be further enhanced by letting the diffusion coefficient depend on the field. A yet less trivial generalization is exemplified by a stylized version of the FitzHugh-Nagumo system, a paradigm of the activator-inhibitor class. After discussing for this system the second aspect enumerated above, we derive from it -through an adiabatic-like elimination of the inhibitor field- an effective scalar model that includes a nonlocal contribution. Studying the role played by the range of the nonlocal kernel and its effect on stochastic resonance, we find an optimal range that maximizes the system's response.