The exact expression of the first moment and the signal-to-noise ratio (SNR) have been calculated for a linear system subject to an external periodic field as well as a multiplicative asymmetric dichotomous noise, by using the Shapiro-Loginov formula. It has been found that the amplitude of the output signal, and the SNR, respectively, exhibit two kinds of the phenomena of stochastic resonance: one is as the functions of the parameters of the asymmetric dichotomous noise, such as the noise strength $D$, and the parameter $k$ describing the asymmetric degree of the dichotomous noise; the other is as the function of the parameter of the input signal, such as the input signal frequency $\ensuremath{\omega}$.

Phenomenon of stochastic resonance caused by multiplicative asymmetric dichotomous noise.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

The transient properties of a bistable system are investigated when both the multiplicative noise and the coupling between additive and multiplicative noises are coloured with different correlation time τ 1 and τ 2 . The mean first-passage time (MFPT) is obtained. The numerical computations show that the intensities of additive and multiplicative noises and the coupling strength λ affected the MFPT in the same way, while τ 1 and τ 2 play different roles in the MFPT. The increase of τ 1 can reduce the escape rate, while increase of τ 2 can enhance the escape rate.

Mean first-passage time of a bistable kinetic model driven by two different kinds of coloured noises

The stochastic resonance characteristics of a linear system driven by a signal-modulated noise and an unmodulated noise are studied. Both the signal-modulated noise and the unmodulated noise are additive in nature and they are correlated. Our study shows that the correlation between the two noises leads to stochastic resonance. An exact analytic expression of the signal-to-noise ratio R is obtained. Based on it, some characteristic features of stochastic resonance are revealed. In the final analysis, the existence of a resonance peak of R vs. noise intensity is a noise correlation effect. On the other hand, the existence of a resonance peak of R vs. noise correlation time τ exhibits a signal-modulated effect of noise. It should be emphasized that the resonance peak of the R-τ curve exists even for uncorrelated noises. This is very different from the case of dependence on the noise strengths.

http://iopscience.iop.org/article/10.1209/epl/i2003-00112-5/pdf

Stochastic resonance in a linear system with signal-modulated noise

The stochastic resonance in an over-damped linear system due to dichotomous noise modulated by a bias signal is studied in detail. By the theory of signal-to-noise ratio (SNR) and the Shapiro–Loginov formula, the exact expressions of the first two moments and SNR for the output to the asymmetric dichotomous noise input are obtained. It is found that each curve of the SNR versus the multiplicative noise intensity exhibits a mono peak and the conventional stochastic resonance appears, which is absent for the case of noise and periodic signal introduced additively. Meanwhile, the SNR is a non-monotonic function of the signal frequency or the correlation time of noise, and the bona fide stochastic resonance (SR) and SR in a broad sense exist. Moreover, the SNR depends on the additive noise intensity, cross-correlation strength and asymmetry of multiplicative noise.

http://iopscience.iop.org/article/10.1088/0305-4470/38/17/002/pdf

Stochastic resonance in linear system due to dichotomous noise modulated by bias signal

We present an analytic investigation of the signal-to-noise ratio by studying the linear model of a single-mode laser driven by coloured pump noise (τ1) and coloured quantum noise (τ2) with coloured cross-correlation (τ3), and obtain an exact analytic expression of the signal-to-noise ratio. We detect that the stochastic resonance occurs when the noise correlation coefficient λ<0. Furthermore, we analyse the effect of τ1,τ2 and τ3 on the signal-to-noise ratio, and derive the condition under which the stochastic resonance occurs.

Stochastic Resonance in Linear Regime of a Single-Mode Laser

We present an analytical investigation of the signal-to-noise ratio (SNR) by studying the bistable sawtooth system driven by correlated Gaussian white noise. The analytic expression of the SNR is obtained. We detect some novel results, as follows. (1) Stochastic resonance (SR) always occurs in the SNR-Q (the multiplicative noise intensity) curve for the whole range of correlation coefficients. (2) There is not only resonance but also suppression and monotony in the dependence of SNR upon the additive noise intensity. (3) There are two extrema (one is minimum, the other maximum) in the SNR-b (the barrier height) curve for different multiplicative noise intensities.

https://iopscience.iop.org/article/10.1088/0256-307X/19/10/306/pdf

Stochastic resonance in a bistable sawtooth potential driven by correlated multiplicative and additive noise

The influences of the two forms of modulated noises, i.e. the bias signal-modulated noise and the direct signal-modulated noise, on the normalized intensity fluctuation (NIF) are investigated, and the results of the two forms of modulation are compared in detail. We find that a minimum for the case of the bias signal modulation appears in the curve of the dependence of the NIF upon the quantum and pump noise intensities when the correlation coefficient between the quantum noise and the pump noise is negative. However, the NIF for the case of the direct signal modulation is independent of the correlation coefficient between the two noises. Moreover, at the same parameter region, the NIF for the bias signal modulation is only one-eighth as much as that for the direct signal modulation.

https://iopscience.iop.org/article/10.1088/0256-307X/21/2/009/pdf

Influences of Modulated Noise on Normalized Intensity Fluctuation in a Single-Mode Laser

Multiplicatively introducing the noise and the signal into the gain-noise model of a single-mode laser system, we detect the two forms of stochastic resonance (the single-peak form stochastic resonance and stochastic multiresonance) in the curve of the dependence of signal-to-noise ratio upon the noise correlation time. Moreover, when the correlation coefficient and the intensities of both noises are changed, the two forms of stochastic resonance alternate.

Stochastic multiresonance for periodically modulated noise in a single-mode laser

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.

Stochastic resonance of bias signal-modulated noise in a single-mode laser

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