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.