Stochastic resonance in a bias linear system with multiplicative and additive noise

In this paper, the stochastic resonance in a bias linear system subjected multiplicative and additive dichotomous noise is investigated. Using the linear-response theory and the properties of the dichotomous noise, this paper finds the exact expressions for the first two moments and the signal-to-noise ratio （SNR）. It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive noise, and it varies non-monotonously with the intensity and asymmetry of the multiplicative noise as well as the external field frequency. Moreover, the SNR depends on the system bias, the intensity of the cross noise between the multiplicative and additive noise, and the strength and asymmetry of the additive noise.     

Stochastic Resonance in an Asymmetric Mono-stable System Subject to Two Periodic Forces and Multiplicative and Additive Noise

The phenomenon of stochastic resonance （SR） in an asymmetric mono-stable system subject to two external periodic forces and multiplicative and additive noise is investigated. It is shown that the signal-to-noise ratio （SNR） for the fundamental and higher harmonics is a non-monotonic function of the intensities of the multiplicative and additive noise, as well as of the system parameter. Moreover, the SNR for the fundamental harmonic decreases with the increase of the system asymmetry, while the SNR for the higher harmonics behaves non-monotonically as the system asymmetry varies.     

Stochastic Resonance in a Time-Delayed Bistable System Driven by Square-Wave Signal

Stochastic resonance in a time-delayed bistable system subject to asymmetric dichotomous noise and multiplicarive and additive white noise is investigated. Using small time delay approximation, we obtain the expression of the signal-to-noise ratio （SNR）. It is found that the SNR is a non-monotonic function of the delayed times, of the amplitude of the input square-wave signal, as well as of the asymmetry of the dichotomous noise. In addition, the SNR varies non-monotonously with the system parameters, with the intensities of the multiplicative and additive noise, as well as with the correlate rate of the dichotomous noise.     

Stochastic resonance in a time-delayed bistable system subject to multiplicative and additive noise

This paper investigates the stochastic resonance in a time-delayed bistable system subjected to multiplicative and additive white noise and asymmetric dichotomous noise.Under the adiabatic approximation condition,the expression of the signal-to-noise ratio (SNR) is obtained.It finds that the SNR is a non-monotonic function of the delayed times,of the amplitude of the driving square-wave signal,as well as of the asymmetry of the dichotomous noise.In addition,the SNR varies non-monotonously with the intensities of the multiplicative and additive noise as well as the system parameters.Moreover,the SNR depends non-monotonically on the correlate rate of the dichotomous noise.     

Stochastic Resonance in a Time-Delayed Mono-Stable System with Multiplicative and Additive Noise

The stochastic resonance （SR） in a time-delayed mono-stable system driven by multiplicative white noise, additive white noise, additive dichotomous noise as well as a periodic square-wave signal is considered from the view of the signal-to-noise ratio （SNR）. It is found that the SNR increases monotonically with the increase of the delay time. The SNR exhibits the SR behavior when it is plotted as a function of intensities of the noises, displaying the asymmetry of the dichotomous noise. The SNR varies non-monotonically with the increase of the system parameter and the amplitude of the input square-wave signal.     

Effect of Time-Delay in the Logistic Growth Model Driven by Weak Signal and White Noise

Effect of delayed time in the logistic growth model subject to weak periodic signal and correlated multiplicative and additive white noise is investigated. Using small time delay approximation, we obtain the expression of the signal-to-noise ratio （SNR）. It is found that the SNR is non-monotonic functions of the delayed times, the system parameters, the intensities of the multiplicative and additive noise, as well as the correlation strength of the two noises.     

Stochastic resonance in linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance （SR） is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR： the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio （SNR） is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.     

Stochastic resonance in a monostable system driven by square-wave signal and dichotomous noise

<正>This paper investigates the stochastic resonance in a monostable system driven by square-wave signal,asymmetric dichotomous noise as well as by multiplicative and additive white noise.By the use of the properties of the dichotomous noise,it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition.It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise,and which varies non-monotonously with the intensity of the multiplicative and additive noise as well as the system parameters.Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.     

A Demonstration of Equivalence between Parameter-Induced and Noise-Induced Stochastic Resonances with Multiplicative and Additive Noises

A typical bistable nonlinear system with multiplicative and additive noises can produce stochastic resonance （SR） by increasing the intensity of the additive noise or the multiplicative noise and it has been proved that SR can also be realized by tuning system parameters. We clearly demonstrate the equivalence between parameter-induced SR （PSR） and noise-induced SR in the presence of multiplicative and additive noises. By tuning several system parameters with fixed noise intensities, the SR is induced just as it is realized by tuning the additive noise or the multiplicative noise. It may be interesting to realize PSR when the noise intensity exceeds the resonance level, or when the characteristic of the noise is unknown.     

Stochastic Resonance in an Asymmetric Bistable System Subject to Frequency Mixing Periodic Force and Noise

The phenomenon of stochastic resonance (SR) in an asymmetric bistable system subject to the multiplicative and additive white noises and two periodic fields is investigated. Using the two-state theory, analytic expressions of the signal-to-noise ratio (SNR) for fundamental harmonics and higher harmonics are derived. It is found that SR appears at both fundamental harmonics and mixed harmonics (of second- and third-order approximation).Moreover, the higher the order of mixed harmonics is, the larger the SNR values are. The effects of static asymmetry on the SNR (of second- and third-order approximation) are different, and the noise intensity ratio can enhance the SNR for higher harmonics.