Stochastic Resonance: influence of a $f^{-\kappa}$ noise spectrum

TL;DR

This paper investigates how different spectral densities of noise, specifically $f^{-erkappa}$, influence stochastic resonance in a double-well potential, using an extended analytical approximation and numerical validation.

Contribution

It extends a previous procedure to analyze stochastic resonance with $f^{-erkappa}$ noise spectra and develops an effective Markovian approximation for systematic study.

Findings

Analytical and numerical results show good qualitative agreement.

The effective Markovian approximation accurately captures the general trends.

The study reveals how noise spectral density affects stochastic resonance.

Abstract

Here, in order to study \textit{stochastic resonance} (SR) in a double-well potential when the noise source has a spectral density of the form $f^{-\kappa}$ with varying $\kappa$, we have extended a procedure, introduced by Kaulakys et al (Phys. Rev. E \textbf{70}, 020101 (2004)). In order to have an analytical understanding of the results, we have obtained an effective Markovian approximation, that allows us to make a systematic study of the effect of such kind of noises on the SR phenomenon. The comparison of numerical and analytical results shows an excellent qualitative agreement indicating that the effective Markovian approximation is able to correctly describe the general trends.