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

## TL;DR

This paper explores stochastic resonance in reaction-diffusion systems using the nonequilibrium potential framework, revealing how system size, diffusion dependence, and nonlocal interactions can enhance the resonance effect.

## Contribution

It extends the nonequilibrium potential formalism to reaction-diffusion systems, analyzing system-size, array, and nonlocal effects on stochastic resonance with new analytical and modeling approaches.

## Key findings

- System-size stochastic resonance naturally emerges in the framework.
- Diffusion coefficient dependence can further enhance stochastic resonance.
- Optimal nonlocal kernel range maximizes system response.

## Abstract

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.