2006
DOI: 10.1103/physreve.74.022102
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Stochastic resonance in a linear system: An exact solution

Abstract: Multistable systems can exhibit stochastic resonance which is characterized by the amplification of small periodic signals by additive noise. Here we consider a nonmultistable linear system with a multiplicative noise forced by an external periodic signal. The noise is the sum of a colored noise of mean value zero and a noise with a definite sign. We show that the system exhibits stochastic resonance through the numerical study of an exact analytical expression for the mean value obtained by functional integra… Show more

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Cited by 35 publications
(8 citation statements)
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“…The simplest nontrivial setup is a Brownian particle in a harmonic external trapping potential with a time-dependent prefactor. This model has been extensively studied as the Brownian parametric oscillator [5,6] and as a basic model for multiplicative noise [7][8][9][10][11], for stochastic resonance [12,13], and for fluctuation squeezing [14]. More recently, it has become popular to use this model to discuss the efficiency of nonequilibrium work production [15,16] and stochastic heat engines [17,18].…”
Section: Introductionmentioning
confidence: 99%
“…The simplest nontrivial setup is a Brownian particle in a harmonic external trapping potential with a time-dependent prefactor. This model has been extensively studied as the Brownian parametric oscillator [5,6] and as a basic model for multiplicative noise [7][8][9][10][11], for stochastic resonance [12,13], and for fluctuation squeezing [14]. More recently, it has become popular to use this model to discuss the efficiency of nonequilibrium work production [15,16] and stochastic heat engines [17,18].…”
Section: Introductionmentioning
confidence: 99%
“…If the potential is quadratic in x, the corresponding Langevin equation with overdamped Brownian dynamics can be solved analytically. The oscillator with time-dependent frequencies has been exploited in quite different contexts (also with inertia) ranging from the Brownian parametric oscillator [85,86], the study of multiplicative noise (fluctuating frequencies) [87,88,89,90,91], stochastic resonance [92,93] and fluctuation squeezing [94] to the efficiency of stochastic heat engines [95] and the motion of classical particles in electromagnetic traps [96,97]. Here we apply the solution to unstable trapping and study the corresponding escape dynamics of a completely overdamped colloidal particle.…”
Section: Harmonic Potentialsmentioning
confidence: 99%
“…quadratic noise) cases [28][29][30][31][32]. As a matter of fact, quadratic colored noise exists actually in physical systems which have been studied in detail by Luczka [28], Hanggi et al [29], Calisto et al [31], Guo et al [32] and the reference therein. Moreover, both dichotomous noise and trichotomous noise are important colored noises in modeling environmental fluctuation of realistic physical, engineering and biological systems [7], [33][34][35][36][37][38].…”
Section: Introductionmentioning
confidence: 99%
“…Most SR investigations have studied the cases that the environmental fluctuation as the linear function of multiplicative colored noise, except for a few works that studied the quadratic function of multiplicative colored noise (i.e. quadratic noise) cases [28][29][30][31][32]. As a matter of fact, quadratic colored noise exists actually in physical systems which have been studied in detail by Luczka [28], Hanggi et al [29], Calisto et al [31], Guo et al [32] and the reference therein.…”
Section: Introductionmentioning
confidence: 99%