Stochastic Resonance in a Bacterium Growth System Subjected to Colored Noises

We present the logistic growth model to study the stochastic resonance (SR) in a bacterium growth system under the simultaneous action of two externalmultiplicative cross-correlation noises and periodic external forcing. The expression of the signal-to-noise ratio (SNR) for a bacterium growth system is derived by using the theory of SNR in the adiabatic limit. Based on SNR, we discuss the effects of self-correlation time τ₁ and τ₂, cross-correlationtime τ₃ and cross-correlation strength λ on the SNR. It is found that the self-correlation time τ₁ and τ₂, and cross-correlation strength λ enhance the SR of the bacterium growth system, while cross-correlation time τ₃ weakens the SR of the bacterium growth system.     

Stochastic Resonance in a Bistable System Subject to Non-Gaussian and Gaussian Noises

In this paper, we consider the phenomenon of stochastic resonance （SR） in a quartic bistable system under the simultaneous action of a multiplicative non-Gaussian and an additive Gaussian noises and a weak periodic signal. The expression of the signal-to-noise ratio R is derived by applying the two-state theory in adiabatic limit. We discuss the effects of the parameter q indicating the departure of the non-Gaussian noise from the Gaussian noise, the correlation time r of the non-Gaussian noise, and coupling intensity A between two noise terms on the stochastic resonance. It is found that the signM-to-noise ratio of the system, as a function of the additive noise intensity, undergoes the transition from having one peak to having two peaks, and then to having one peak again when the parameter q or the noise correlation time τ is increased. The parameter q and τ play opposite roles in the SR of the system.     

Fokker-Planck Equation of a Stochastic System Driven by Spatially-Related Noises

In this paper we study a general stochastic system driven by the spatially-related Gaussian white noises. The corresponding Fokker-Planck equation is calculated; and some typical cases are analyzed. Finally, by the Fokker-Planck equation derived in the paper we study a single bistable kinetic process with spatially-related noise. The results obtained in the paper provide a correct foundation for the.treatment of the stochastic systems driven by spatially-related noises.     

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance （SR） in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio （SNR） is calculated according to the generalized two-state theory （shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 （1999） 136]）. We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR.     

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance (SR) in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio (SNR) is calculated according to the generalized two-state theory (shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 (1999) 136]). We find that the SNR increases with the proximity of a to zero. In addition, the correlation time τ between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time τ between the Gaussian additive colored noise is, the higher of the peak value of SNR.     

Extinction Time of a Metapopulation Driven by Colored Correlated Noises

The simplified incidence function model which is driven by the colored correlated noises is employed to investigate the extinction time of a metapopulation perturbed by environments. The approximate Fokker-Planck Equation and the mean first passage time which denotes the extinction time （Tex） are obtained by virtue of the Novikov theorem and the Fox approach. After introducing a noise intensity ratio and a dimensionless parameter R = D /α （D and a are the multiplicative and additive colored noise intensities respectively）, and then performing numerical computations, the results indicate that： （i） The absolute value of correlation strength A and its correlation time τ3 play opposite roles on the Tex; （ii） For the case of 0 〈λ〈 1,α and its correlation time τ2 play opposite roles on the Tex in which R〉 1 is the best condition, and there is one-peak structure on the Tex - D plot; （iii） For the case of-1 〈 λ≤ 0, D and its correlation time τ1 play opposite roles on the Tex in which R 〈 1 is the best condition and there is one-peak structure on the Tex - τ2 plot.     

Stochastic Resonance in a Single-Mode Laser Driven by Quadratic Colored PumpNoise: Effects of Biased Amplitude Modulation Signal

A single-mode laser noise model driven by quadratic colored pump noise andbiased amplitude modulation signal is proposed. The analytic expression ofsignal-to-noise ratio is calculated by using a new linearized procedure. Itis found that there are three different typies of stochastic resonance inthe model: the conventional form of stochastic resonance, the stochasticresonance in the broad sense, and the bona fide SR.     

Effect of Correlation of Two Dichotomous Noises on Stochastic Resonance

The effect of the correlation of two dichotomous noises on stochastic resonance is investigated for a linear stochastic system subject to a periodic oscillatory signal. It is found that, the correlation between the two dichotomous noises can not only affect the appearance of the stochastic resonance phenomenon, but also the distinctness of the stochastic resonance phenomenon. There is an optimal value of the correlation, at which the stochastic resonance phenomenon is most distinct. In addition, the correlation between the two dichotomous noises can also cause the movement of the peak of stochastic resonance. Finally, two stochastic resonances caused by two correlated multiplicative dichotomous noises can be found in this system.     

Effects of Self-Correlation Time and Cross-Correlation Time of Additive and Multiplicative Colored Noises for Dynamical Properties of a Bistable System

Considering a bistable system driven by additive and multiplicative colored noises with colored cross-correlation, we obtain the analytic expressions of the stationary probability distribution P _st(x), the linear relaxation time T _c , and the correlated function C(s). The effects of the noise intensity, the self-correlation time and the cross-correlation time for the bistable system are discussed. The noise intensity D speeds up relaxation of the system from unstable points, which when D < Q, the effects are the most obvious; when D > Q, the effects are damped. The self-correlation time τ₁ and τ₂ make the stationary probability distribution of the dynamical variable x be shaper and speed up the fluctuation decay of the dynamical variable x. On the contrary, the cross-correlation time τ₃ makes the stationary probability distribution of the dynamical variable x be flatter and slows down the fluctuation decay of the dynamical variable x. The effect of the self-correlation time is more projecting than the effect of the cross-correlation time. PACS number: 05.40.−a, 02.50.−r, 05.10.Gg.     

Stochastic Resonance in a Bistable System with Time-Delayed Feedback Loops

The phenomenon of stochastic resonance of a bistable system subjected to linear time-delayed feedback loops driven by multiplieative Gaussian coloured noise and additive Gaussian white noise is investigated. Firstly, the analytic expression of the quasi-steady distribution function Ps （x, t） is derived by applying the unified coloured noise approximation and the Novikov Theorem; Secondly, the expression of the signal-to-noise ratio （SNR） is obtained in the adiabatic limit to quantify the stochastic resonance. Finally, tile effects of the linear coefficient a, the nonlinear coefficient b, the linear time-delayed feedback coefficient c and the delay time r on Ps（x,t） and SNR^± are discussed. It is found that the effects of the linear coefficient and the nonlinear coefficient, the positive linear time-delayed feedback coefficient and the negative linear time-delayed feedback coefficient, the positive delayed time and the negative delayed time on Ps（x,t） and SNR^± are different, respectively. This discussion would be helpful to the study of the system reliability and controlling stochastic resonance.     

Stochastic Resonance in a Bistable System Subject to Dichotomous Noise

The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise （DN） is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-tonoise ratio （SNR） and the spectral power amplification （SPA） have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.     

Stochastic Resonance in a Bistable System Subject to Dichotomous Noise

The stochastic resonance phenomenon in a bistable system subject to Markov dichotomous noise (DN) is investigated. Based on the adiabatic elimination and the two-state theories, the explicit expressions for the signal-to-noise ratio (SNR) and the spectral power amplification (SPA) have been obtained. It is shown that two peaks can occur on the curve of SNR versus the intensity of the DN. Moreover, the SNR is a non-monotonic function of the correlation time of the DN. The SPA varies non-monotonously with the strength of the DN. The dependence of the SNR on the frequency and the amplitude of the external periodic signal are discussed. The effect of the external frequency and the correlation time of the DN on the SPA are analyzed.     

Appearance of Stochastic Resonance in Protein Motor System

A protein motor system driven by sine electric field is investigated. The signal-to-noise ratio （SNR） is derived in the adiabatic limit. The phenomenon of stochastic resonance is found for this protein motor system.     

Effect of Asymmetry in a Bistable System Subject to Multiplicative Colored Noise

By the method of the stochastic energetics, we investigate the stochastic resonance (SR) phenomenon of an overdamped Brown particle in an asymmetric bistable potential, driven by external periodical signal and multiplicative noise. The expressions have been obtained for the quasi-steady-state probability distribution function. It is found that the input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of the noise strength, whereas the IE turns to be a monotonic function of the correlation time of the noise. The effect of potential asymmetry is also studied on SR and IE.     

Stochastic Resonance in a Spatially Symmetric and Flashing Periodic Potential Subjected to Correlated Noises

A Brownian particle in a spatially symmetric and flashing periodic potential subjected to correlated noises is investigated. The exact expression of its current is analytically derived. The numerical results indicate that its current as a function of noise intensity exhibits two peaks in the case of positive correlations, and two vales in the case of negative correlations, i.e., a novel stochastic resonance （SR） phenomenon. The SR is attributed to the harmonic cooperation between the noises and the flashing periodic potential. The conditions under which the SR occurs are also presented.     

Multiplicative Stochastic Resonance for a Linear System Driven by O-U Noise

In the paper, we study a linear system driven by O-U noise and give a method which is different from the one stated in Europhys. Lett. 40 （1997） 117. We find the same phenomenon of multiplicative stochastic resonance for the response of the system to the signal as the one found in Europhys. Left. 40 （1997） 117. The merit of our method is that it prevents the complex formulas when making sum from n = 0 to n →∞ as in Europhys. Lett. 40 （1997） 117, which leads to the approximate results of the figures.     

Stochastic resonance in an asymmetric bistable system driven by coloured noises

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises.The approximate Fokker-Planck equation is derived based on the Novikov theorem and the Fox approach.By applying the two-state theory,the expression of the signal-to-noise ratio is obtained in the adiabatic limit.The effects of the noise parameters on signal-to-ratio are discussed.It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.     

Two Stochastic Resonances Induced by Two Different Multiplicative Telegraphic Noises for an Electric System

In this paper, an electric system with two dichotomous resistors is investigated. It is shown that this system can display two stochastic resonances, which are the amplitude of the periodic response as the functions of the two dichotomous resistors strengthes respectively. In the limits of Gaussian white noise and shot white noise （i.e., the two noises are both Gaussian white noise or shot white noise） no phenomena of resonance appear. By further study, we find that when the system is with three or more multiplicative telegraphic noises, there are three or more stochastic resonances.     

Stochastic Resonance of a Periodically Driven Bistable System with Two Different Kinds of Time Delays

In this paper, we study the phenomenon of stochastic resonance （SR） in a periodically driven bistable system with correlations between multiplicative and additive white noise terms when there, are two different kinds of time delays existed in the deterministic and fluctuating forces, respectively. Using the small time delay approximation and the theory of signal-to-noise ratio （SNR） in the adiabatic limit, the expression of SNR is obtained. The effects of the delay time T in the deterministic force, and the delay time 8 in the fluctuating force on SNR are discussed. Based on the numerical computation, it is found that： （i） There appears a reentrant transition between one peak and two peaks and then to one peak again in the curve of SNR when the value of the time delay θ is increased. （ii） SR can be realized by tuning the time delay T or 8 with fixed noise, i.e., delay-induced stochastic resonance （DSR） exists.