Stochastic resonance in linear systems subject to multiplicative and additive noise

Abstract

Exact expressions have been found for the first two moments and the correlation function for an overdamped linear system subject to an external periodic field as well as to multiplicative and additive noise. Stochastic resonance is absent for Gaussian white noise. However, when the multiplicative noise has the form of an asymmetric dichotomous noise, the signal-to-noise ratio (SNR) becomes a nonmonotonic function of the correlation time and the asymmetry of noise. Moreover, the SNR turns out to be a nonmonotonic function of the frequency of the external field as well as strongly depending on the strength of the cross correlation between multiplicative and additive noise.

Effect of Correlated Dichotomous Noises on Stochastic Resonance in a Linear System

“…In addition, two correlated multiplicative dichotomous noises can cause two types of SRs in a linear system [38]. Reference [39] investigated effect of correlated noises on the linear system without a bias force, and pointed out that in the case of asymmetric multiplicative noise, the system's SNR becomes a nonmonotonic function of correlation time of the multiplicative noise, and increases with the correlation strength between multiplicative and additive noises.…”

Stochastic resonance in a stochastic bistable system subject to additive white noise and dichotomous noise

“…The SR phenomenon has been studied in a variety of nonlinear systems with additive and multiplicative noise [1][2][3][4][5][6][7][8][9]. It was concluded that nonlinearity, periodic forces and random forces are the essential ingredients for the onset of SR. On the other hand, behavior similar to SR has also been found in linear systems subject to multiplicative noise [10][11][12][13]. Gora [13] established a genuine SR in a linear system subject to mutually correlated additive and multiplicative white noises.…”

Stochastic resonance in a harmonic oscillator with fractional-order external and intrinsic dampings

“…First of all, most of the literatures considered the nonlinearity to be an essential condition to generate SR. However, recent investigations show that SR was also found in linear systems driven by multiplicative noise [9][10][11]. Secondly, the conventional SR means that the signal-to-noise ratio (SNR) versus the noise intensity exhibits a peak [12,13], while the generalized SR which was introduced by Gitterman [14][15][16] usually implies the non-monotonic behaviors of certain functions of the output signal (such as moments, amplitude, autocorrelation function, signal power amplification factor and SNR) on the noise and system parameters.…”