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

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.

Stochastic Resonance in a Harmonic Oscillator Fluctuating Intrinsic Frequency by Asymmetric Dichotomous Noise

The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov formula, the exact solution of the average output amplitude gain （OAG） is obtained. Numerical results show that OAG depends non-monotonically on the noise characteristics： intensity, correlation time and asymmetry. The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time.

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.

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

在易于二外部周期的力量、趋于增加的一个不对称的单稳态的系统和添加剂噪音的随机的回声(SR ) 的现象被调查。为基本、更高的泛音的 signal-to-noise 比率(SNR ) 是紧张的一个非单调的函数，这被显示出趋于增加并且添加剂噪音，以及系统参数。而且，为基本泛音的 SNR 随系统不对称现象的增加减少，当为更高的泛音的 SNR 是 non-monotonically 表现时，系统不对称现象变化。

Stochastic resonance in a stochastic bistable system with additive noises and square-wave signal

This paper considers the stochastic resonance in a stochastic bistable system driven by a periodic square-wave signal and a static force as well as by additive white noise and dichotomous noise from the viewpoint of signal-to-noise ratio. It finds that the signal-to-noise ratio appears as stochastic resonance behaviour when it is plotted as a function of the noise strength of the white noise and dichotomous noise, as a function of the system parameters, or as a function of the static force. Moreover, the influence of the strength of the stochastic potential force and the correlation rate of the dichotomous noise on the signal-to-noise ratio is investigated.

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.

Entropic stochastic resonance in a confined structure driven by dichotomous noise and white noises

The entropic stochastic resonance （ESR） in a confined system subjected to dichotomous noise and white noise and driven by a periodic sinusoidal force along the x axis of the structure and a time-dependent force in the declining direction, is investigated. Under the adiabatic approximation condition and based on the two-state theory, the expression of the output signal-to-noise ratio （SNR） is obtained. The results show that the SNR is a non-monotonic function of the strengths of dichotomous noise, white noise, and correlated strength of correlated noise. In addition, the SNR varies non-monotonically with the increase of the shape parameters of the confined structure, and also with the increase of the constant force along the y axis of the structure. The influence of the correlation rate of the dichotomous noise, and that of the frequency of the periodic force on the SNR are discussed.

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.

Effect of Correlation of Two Dichotomous Noises on Stochastic Resonance

随机的回声上的二两分的噪音的关联的效果为一个线性随机的系统题目被调查到一个周期的摆动的信号。它被发现那，在二两分的噪音之间的关联不能仅仅影响随机的回声现象的随机的回声现象，而且不同的外观。有关联，随机的回声现象在是很不同的最佳的价值。另外，在二两分的噪音之间的关联能也引起随机的回声的山峰的运动。最后，二引起的二随机的回声相关趋于增加的两分的噪音能在这个系统被发现。

Stochastic Resonance Induced by an Asymmetric Two-state Noise

Stochastic resonance (SR) phenomenon of the system that is subject to the asymmetric two-state noise is investigated from the broad sense. It is shown that the amplitudes of the output signal exhibit the non-monotonic dependence on the input signal frequency ω, and the parameters describing the asymmetric two-state noise, such as the transition rate λ, the order parameter k describing the asymmetric degree of the two-state noise, and the noise strength D.

Experiment and application of parameter-induced stochastic resonance in an over-damped random linear system

This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed. Several potential applications of parameter-induced stochastic resonance are given in circuits.

Stochastic Huge-Resonance Caused by Coupling for a Globally Coupled Linear System

在纸，我们与易于时间的周期的力量并且与趋于增加的两分的噪音的有限子单元调查一个全球性联合的线性系统。它被看那，在子单元之中的全球联合能巨大地分别地作为信号的频率的函数作为噪音和那的转变率的函数为平均的吝啬的域的振幅提高 SR 的现象。

Frequency(Stochastic) Resonance and Stochastic Resonance for a Superconducting Junctions' Device

In this paper, we investigate a Josephson-junction device with dichotomous resistance or a special SQUID(superconducting quantum interference device). It is shown that frequency(stochastic) resonance and stochastic resonance can appear for some suitably selected parameters' values of the device respectively. Our results can provide some insights for the investigation of the SQUID response to the signal(including the input alternating current, the added alternating voltage, the vertically added alternating magnetic field, and the detected(electric-magnetic) temporal-periodic signal).

Lévy噪声和高斯白噪声共同激励的非对称三稳系统的随机共振

将Lévy噪声和高斯白噪声引入非对称三稳系统模型中,采用数值方法计算不同参数下系统的信噪比,分析噪声参数、系统参数以及信号振幅对系统随机共振现象的影响机制.研究结果表明,较大的稳定性指标、偏斜参数、3次刚度系数以及信号振幅会抑制随机共振现象的发生,而较大的非对称参数则会促进随机共振现象的发生.特别地,当信噪比作为加性噪声强度的函数时,较大的5次刚度系数不易于出现随机共振现象,而当信噪比作为乘性噪声强度的函数时,情况则相反,即5次刚度系数越大越容易发生随机共振现象.

α稳定噪声下时滞非对称单稳系统的随机共振

将α稳定噪声与单稳系统相结合,分别研究了不同α稳定噪声环境下的无时滞项和有时滞项的非对称单稳系统的随机共振。利用数值仿真说明了在无时滞项和有时滞项的非对称单稳系统中均存在随机共振现象,并讨论了α稳定噪声特征指数α(0<α≤2)、对称参数β(-1≤β≤1)、单稳系统参数a、乘性噪声放大系数D、非对称系数r及时滞量τ对系统信噪比增益的影响。

Levy噪声驱动下指数型单稳系统的随机共振特性分析

该文基于绝对值型和指数型势函数,构建了更一般的指数型单稳势函数,深入研究了Levy噪声驱动的指数型单稳系统,并总结出不同特征指数a和不同对称参数b下,指数型系统参数l和b,Levy噪声强度系数D对指数系统共振输出的作用规律。研究表明:在不同Levy噪声驱动下,通过调节参数l和b均可诱导随机共振(SR),且当b(或l)的取值越大时,产生较好随机共振效果l(或b)的区间越大,从而改善传统SR系统由于参数选择不当造成随机共振效果不佳的问题。此外,通过调节噪声强度系数D也能产生随机共振,且较好随机共振区间不随a或b变化;最后将指数型单稳系统应用于轴承故障检测,效果明显优于传统双稳系统。

Levy噪声激励下的幂函数型单稳随机共振特性分析

将Levy噪声与幂函数型单稳随机共振系统相结合,为确保实验数据的可靠性,以平均信噪比增益为衡量指标,针对Levy噪声激励下的随机共振现象进行了研究.详细介绍了单稳系统势函数形式及Levy噪声的产生原理,深入探究了不同特征指数α和不同对称参数β取值条件下,单稳系统参数a和b、Levy噪声强度放大系数D对幂函数型单稳系统共振输出的作用规律.研究结果表明,在任意Levy噪声分布条件下,通过对系统参数a和b的适当调整均能诱导随机共振,完成微弱信号检测,且有多个随机共振区间与之对应,同时这些区间不随α或β的改变而改变;此外,在研究噪声诱导的随机共振时也发现了同样的规律,通过调节噪声强度放大系数D也能产生随机共振,且随机共振区间也不随α或β的改变而改变;最后,在研究系统参数a和b之间的相互作用关系时发现,一个系统参数的随机共振取值区间会随着另一个系统参数的改变而改变.所获得的研究结果有效解决了Levy噪声激励下幂函数型单稳随机共振系统的系统参数、噪声强度放大系数的选择问题,为其应用于工程实践提供了可靠的理论依据.

信号调制色噪声作用下线性系统的随机共振

研究系统的阻尼系数受二值噪声扰动时,信号调制二值噪声驱动的二阶过阻尼线性系统的随机共振现象。基于线性系统理论和相关删去法方法,得到了系统平均输出幅度增益的精确表达式。研究表明:系统的输出幅度增益是二值噪声的强度和相关率、系统固有频率、系统阻尼系数,以及激励信号的频率的非单调函数,适当的噪声参数可以使系统的输出幅度增益大于无噪声时的输出幅度增益。

RC串联电路的随机共振

研究了时间常数受非对称双值色噪声扰动的RC串联电路的随机共振现象。利用随机平均法和Shapiro-Loginov公式,得到了平均输出幅度增益的精确表达式。分析表明,平均输出幅度增益是噪声的强度、自相关率和非对称性参数的非单调函数,适当的噪声参数和系统参数可以使平均输出幅度增益取得最小值,输出幅度增益关于噪声非对称性和相关速率的函数的最小值不随信号频率的变化而变化。