A random dynamical systems perspective on stochastic resonance

TL;DR

This paper investigates stochastic resonance in a stochastic Duffing oscillator using random dynamical systems theory, establishing the existence of unique attractors and measures, and introducing an indicator for resonance.

Contribution

It applies the framework of random dynamical systems to analyze stochastic resonance, proving existence of unique attractors and measures in this context.

Findings

Existence of a unique global attracting random periodic orbit.

Existence of a stationary periodic measure.

Introduction of an indicator for stochastic resonance.

Abstract

We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcing. We prove the existence of a unique global attracting random periodic orbit and a stationary periodic measure. We use the stationary periodic measure to define an indicator for the stochastic resonance.