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.     

非线性漂移的Fokker-Planck方程的近似非定态解

研究了由高斯白噪声和色噪声作用下的非线性动力学系统的不稳定态演化问题. 在弱噪声极限下, 运用本征值本征矢理论得到了非定态解ρ(x, t)的近似表达式; 分析了色噪声自关联时间τ, 强度α对ρ(x, t)以及对一、二阶矩的影响. 数值模拟发现: 1)t在一定范围内, ρ(x, t)是变量x和t的单调函数, 且随τ的增大而增大, 反之, 随α的增大而减小; 2)一阶矩是τ和α的单调函数, 但二阶矩却是非单调函数, 在参数影响下发生了相变现象. 关键词： 奥恩斯坦-乌伦贝克过程 本征值 本征矢 非定态解     

Mean First-Passage Time in Optical Bistable Systems

The transient properties of an optical bistable system driven by multiplicative and additive noises are investigated. The effects of multiplicative and additive noises intensities on the mean first-passage times （MFPTs） in two opposite directions are discussed. The results show that the intensities of multiplicative and additive noises affect the MFPTs on two directions in the same way.     

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.     

信号调制下分段噪声驱动的线性系统的随机共振

研究了由乘性和加性噪声的线性组合作为调制噪声的线性系统的随机共振.运用平均法,得到了一、二阶矩和信噪比的精确表达式. 通过分析信噪比,在此系统中发现了真实的随机共振、传统的随机共振和广义随机共振.发现在真实的随机共振中,适当地调整参数,共振和抑制会同时出现.此外,还发现对不同的互关联强度,分别选用乘性和加性噪声作为调制噪声能够提高信噪比. 关键词： 随机共振 信噪比 调制噪声 分段噪声     

Current transport and mass separation for an asymmetric fluctuation system with correlated noises

We discuss the transport of an underdamped particle driven by an external fluctuation force in a spatially periodic asymmetric potential with correlated noises. The corresponding mathematical model is established. The movement of the steady current of an underdamped particle is presented by the method of the numerical simulation. It is indicated that the value of the current may be negative, zero, or positive. The external fluctuation force and correlated noises can effect the current direction. Under the appropriate parameters, the correlated noises intensity may even raise a reversal of the current.Besides, we have noticed a phenomenon that particles with different weight have different directions during movement by the impact of the correlated noises and external fluctuation force. Therefore, the Brownian particles can be effectively separated according to their masses.     

光学双稳系统中的随机共振

运用绝热近似理论，研究了由加性噪声和乘性噪声及周期信号驱动的光学双稳系统的随机共振现象. 发现该模型中输出信噪比R～随着加性噪声强度D_a的变化曲线中会出现随机共振现象，而信噪比R～随着乘性噪声强度D_m的变化曲线是单调减小的，信噪比曲线中没有出现随机共振现象. 因此，加性噪声和乘性噪声对输出信噪比的影响是不同的. 关键词： 随机共振 信噪比 乘性噪声 加性噪声     

既非离散又非连续的随机变量

讨论既非离散又非连续的随机变量,总结这类随机变量分布函数的特点,由此可进行这类随机变量类型的判定.通过举例给出既非离散又非连续型随机变量数学期望的求法.     

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.