Stochastic Resonance in Nonpotential Systems

TL;DR

This paper presents an analytical method to demonstrate stochastic resonance in nonpotential systems, applying it to the FitzHugh-Nagumo model to show the phenomenon's occurrence.

Contribution

It introduces a novel analytical approach for identifying stochastic resonance in nonpotential systems, including a reduction to one-dimensional dynamics.

Findings

FitzHugh-Nagumo model exhibits stochastic resonance under periodic forcing.

The method applies to various nonpotential systems.

Analytical demonstration of maximum signal-to-noise ratio.

Abstract

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit, and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.