由加性和乘性噪声驱动的非对称双稳系统的随机共振

根据信噪比理论，研究了由乘性和加性白噪声以及周期矩形信号共同作用的非对称双稳系统的随机共振。推导出了信噪比的解析表达式，并且该表达式适用于任意的信号振幅。数值分析表明乘性噪声强度D和加性噪声强度α对信噪比的影响是不同的：对应于任意的一个非对称系数r的值，SNR-α 曲线比SNR-D曲线更容易出现随机共振。即当系统的双阱不是很不对称的时候，改变加性噪声比改变乘性噪声更容易产生随机共振。此外，势井的非对称性能够减小信噪比。     

非对称双稳系统中平均首次穿越时间的研究

研究了由乘性白噪声和加性白噪声驱动的非对称双稳系统中，势阱的非对称性对两个不同方 向的平均首次穿越时间的影响.发现在非对称双稳系统中，两个不同方向的平均首次穿越时 间是与初始状态有关.此外，对一维非对称达芬模型的平均首次穿越时间进行了研究.数值结 果表明：(1) 非对称双稳系统的平均首次穿越时间对初始状态有“记忆性”；(2) 噪声强度 对两个不同方向的平均首次穿越时间T₊（x_s1→x_s2)和 T_-(x_s2→x_s1)的影响是不同的：lnT_--Ｄ 曲线上存在峰值，出 现了“共振”现象，而lnＴ₊-Ｄ曲线是单调的；(3) 势阱的非对称性r对T ₊（x_s1→x_s2)和T_-(x_s2→x_s1 )的影响是不 同的：lnＴ_--r曲线上存在极小值，出现了“抑制”现象，而lnＴ₊ -r曲线是单调的. 关键词： 平均首次穿越时间 非对称双稳系统 乘性噪声 加性噪声     

Escape rates in underdamped bistable potentials driven by coloured noise

The brownian motion in a quartic double-well potential driven by coloured noise is investigated in the low-viscosity limit by means of analogue simulation. The dependence of the escape rate on the noise correlation-time τ is determined for the conditions simulated: the escape rate decreases exponentially with increasing τ². The relevant law is derived theoretically in the limit of vanishingly small viscosity and high potential barriers.     

Stochastic resonance in an asymmetric bistable system driven by coloured correlated multiplicative and additive noise

This paper investigates the stochastic resonance （SR） phenomenon in an asymmetric system with coupling between multiplicative and additive noise when the coupling between two noise terms is coloured. The approximate expression of signal-to-noise ratio has been obtained by applying the two-state theory and SR exhibits in the bistable system. Moreover, the potential asymmetry r and cross-correlation strength λ can weaken the SR phenomenon, while the cross-correlation time r can strengthen the SR phenomenon.     

色关联噪声驱动的非对称双稳系统中平均首次穿越时间的研究

研究了由色关联的乘性白噪声和加性白噪声驱动的非对称双稳系统中，色关联及非对称性对平均首次穿越时间的影响.数值结果表明乘性噪声强度α和加性噪声强度D及互相关时间τ对首次穿越时间T的影响是一致的，加性和乘性噪声间的互关联强度λ及势阱的非对称性r对T的影响是一致的.τ的增加能提高粒子的逃逸率，λ的增加则减小逃逸率.     

色噪声驱动的非对称双稳系统的平均首次穿越时间

研究了由关联乘性色噪声及加性白噪声驱动的非对称双稳系统中势阱的非对称性及噪声对系统两个方向平均首次穿越时间的影响. 首先利用一致有色噪声近似推导了系统的稳态概率密度的表达式，根据最速下降法推导了平均首次穿越时间的表达式. 数值结果表明：势阱的非对称性对两个方向的平均首次穿越时间的影响是不同的；由于噪声的关联性，即使对于关联乘性色噪声及加性白噪声驱动的对称双稳系统，两个方向的平均首次穿越时间也不再相等；在lnT₊-r和lnT_{-关键词： 平均首次穿越时间 非对称双稳系统 乘性色噪声 加性白噪声}     

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.     

线性调频信号激励过阻尼双稳系统的随机共振现象研究

线性调频信号是工程中常见的一种信号, 由于其为非周期信号, 无法以频域信噪比作为衡量其是否产生随机共振的测量手段, 故鲜有文献研究以线性调频信号为激励信号的随机共振现象. 本文利用线性调频信号在最优分数阶Fourier变换域上的能量聚集性, 首次提出以最优分数阶Fourier变换域上定义的信噪比作为测量手段, 研究了线性调频信号叠加高斯白噪声激励过阻尼双稳系统的随机共振现象, 且发现了以线性调频信号为激励信号时产生的新现象, 即随着信号频率的增大, 随机共振将逐渐减弱, 并给出了合理的解释.仿真的结果与理论分析一致, 验证了本文所提出方法的有效性. 关键词： 线性调频信号 分数阶Fourier变换 随机共振     

关联噪声驱动的非对称双稳系统的随机共振

运用统一色噪声近似理论和两态模型理论,研究了周期矩形信号和关联的乘性色噪声和加性白噪声驱动的非对称双稳系统的随机共振现象,得到了适合信号任意幅值的信噪比表达式.信噪比是乘性噪声强度、加性噪声强度、乘性噪声自关联时间、噪声耦合强度的非单调函数,所以该双稳系统中出现了随机共振.同时,调节加性噪声强度比调节乘性噪声强度更容易产生随机共振.势阱静态非对称性和噪声之间的耦合强度对信噪比的影响是不同的. 关键词： 非对称双稳系统 随机共振 信噪比 周期矩形信号     

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

We present an analytic investigation of the signal-to-noise ratio (SNR) by studying the bistable sawtooth system driven by correlated Gaussian white noises. The analytic expression of SNR is obtained. Based on it, we detect the phenomenon of stochastic multiresonance, which arises from the dependence of SNR upon the noises correlation coefficient. Furthermore, there exists not only resonance, but also suppression in the SNR∼D (the additive noise intensity) curve and the SNR∼Q (the multiplicative noise intensity) curve. Received 26 February 2002 / Received in final form 12 July 2002 Published online 17 September 2002     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

Mean first-passage time of an asymmetric bistable system driven by colour-correlated noise

In this paper, the effect of every parameter (including p, q, r, \la, \tau) on the mean first-passage time (MFPT) is investigated in an asymmetric bistable system driven by colour-correlated noise. The expression of MFPT has been obtained by applying the steepest-descent approximation. Numerical results show that (1) the intensity of multiplicative noise p and the intensity of additive noise q play different roles in the MFPT of the system, (2) suppression appears on the curve of the MFPT with small \la (e.g. \la<0.5) but there is a peak on the curve of the MFPT when \la is big (e.g. \la >0.5), and (3) with different values of r (e.g. r=0.1, 0.5, 1.5), the effort of \tau on the MFPT is diverse.     

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance(SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory(LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density(PSD) and signal-to-noise ratio(SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.     

Correlation function of an optical bistable system with cross-correlated additive white noise and multiplicative colored noise

Considering an optical bistable system with cross-correlated additive white noise and multiplicative colored noise, we study the effects of correlation between the noises on the correlation function C（s） using the unified colored noise approximation and the Stratonovich deeoupling ansatz formalism. The effects of the self-correlation time τ of the multiplicative colored noise and the correlation intensity λ between the two noises are studied with numerical calculation. It is found that C（s） increases with the increase of the self-correlation timeτ, but decreases with the increase of the correlation intensity λ. At large value of τ, there is almost no change for C（s） when τ changes.     

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.     

Associated relaxation time and intensity correlation function of a bistable system driven by cross-correlation additive and multiplicative coloured noise sources

The associated relaxation time and the intensity correlation function of a bistable system driven by an additive and a multiplicative coloured noise with coloured cross-correlation are investigated. Using the Novikov theorem and the projection operator method, the analytic expressions of the stationary probability distribution P_st(x), the relaxation time T_c, and the normalized correlation function C(s) of the system are obtained. The effects of the noise intensity, the cross-correlation strength λ and the cross-correlation time τ are discussed. By numerical computation, it is found that the cross-correlation strength |λ| and the quantum noise intensity D decrease the relaxation of the system from unstable points. The cross-correlation time τ delays relaxation of the system from unstable points. The cross-correlation strength λ and the cross-correlation time τ can alter the effects of the pump noise intensity Q. Thus, the relaxation time T_c is a stochastic resonant phenomenon, and distribution curves exhibit a single-maximum structure.     

Stochastic resonance in linear system driven by multiplicative and additive noise

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation function and the SR phenomenon appeared. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the asymmetry of multiplicative noise has different effect on signal-to-ratio (SNR) for the first two different forms of SR and the effects of multiplicative noise and additive noise on SNR are different.     

Stochastic resonance in an optical bistable system subjected to cross-correlated additive white noise and multiplicative colored noise

The stochastic resonance (SR) of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio (SNR). Results show that cross-correlation intensity λ enforces the SR of the system. The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ (τ is the self-correlation time of the multiplicative colored noise). We find the SR phenomenon in the SNR-D and SNR-Q curves (D and Q are the intensities of the additive and multiplicative noises, respectively), but not in the SNR-λ curves.     

非高斯噪声驱动下非对称双稳系统的平均首次穿越时间与随机共振研究

研究了乘性非高斯噪声和加性高斯白噪声共同激励下非对称双稳系统的平均首次穿越时间和随机共振问题. 利用路径积分法和两态模型理论,推导出平均首次穿越时间和信噪比的表达式. 研究结果表明:势阱非对称性对两个不同方向的平均首次穿越时间的影响是不同的. 信噪比是加性噪声强度和势阱非对称性的非单调函数,系统出现了随机共振现象;信噪比是乘性噪声强度的单调函数,没有共振峰出现. 这说明该系统中乘性噪声强度和加性噪声强度对信噪比的影响是不同的. 关键词： 非高斯噪声 非对称双稳系统 平均首次穿越时间 随机共振     

Stochastic resonance induced by bounded noise and periodic signal in an asymmetric bistable system

Stochastic resonance (SR) induced by the bounded noise in an asymmetric bistable system is investigated. Based on stochastic simulation, the signal power amplification SPA$SPA$ is derived for the case of the additive modulated signal. The simulation results indicate that: (1) the SR phenomenon is weakened by the asymmetry of the system; (2) increasing the frequency ω$\omega$ restricts the SR of the system; (3) there is an optimum value of amplitude A$A$ matching the strongest SR phenomenon.