关联白噪声驱动的具有时间延迟的Logistic系统

关联白噪声驱动的具有时间延迟的Logistic系统可更真实的反映肿瘤细胞的增长问题,本文通过小时间延迟近似方法对由关联白噪声驱动的具有时间延迟的Logistic系统进行了研究,得到了系统的稳态概率密度,并进一步分析了加性和乘性噪声强度,噪声关联时间和时间延迟对稳态概率密度的影响以及噪声诱导的非平衡相变现象. 关键词： Logistic系统 关联白噪声 时间延迟 非平衡相变     

白交叉关联色噪声驱动的线性振子的扩散

研究了由白交叉相关的两色噪声所驱动的线性振子的扩散,其中一个噪声受偏置的周期信号所调制.揭示了乘性色噪声的自关联时间τ1和加性色噪声的自关联时间τ2对d-Q,d-D及d-Ω曲线的影响,其中d,Q,D和Ω分别为振子的扩散系数、受信号调制的噪声强度、未受调制的噪声强度和信号的频率.发现d-Q和d-D曲线均存在一个极小值,而d-Ω曲线则在Ω=～Ω处呈现极大值,～Ω为振子频率.推导了使扩散系数d=0的条件.     

色关联噪声驱动下双模激光随机共振

运用线性近似方法,计算得到了关联色噪声和输入周期信号作用下双模激光增益模型输出信号光强的功率密度谱和信噪比,讨论了信噪比随系统参数的变化关系.研究结果发现:在系统的参数和输入信号的频率满足一定条件时,信噪比不仅随噪声强度变化出现了传统的随机共振现象,还发现其随自饱和系数c2、输入信号频率°及交叉耦合参数b的变化都出现了随机共振.     

交叉色关联噪声驱动的单模激光系统统计性质研究

采用交叉色关联的加性色噪声和乘性色噪声驱动的单模激光立方模型,通过诺维科夫理论和福克斯近似以及斯特拉托诺维奇近似,得到反映激光统计性质的强度关联函数C的表达式;研究关联时间τ、净增益系数a₀和交叉关联强度λ对强度关联函数C的影响.数值模拟发现,在阈值以上（a₀>0）时,关联函数C随关联时间τ的增大而增大;在阈值以下（a₀<0）时,关联函数C随关联时间τ的增大而减小.无论在阈值以上还是阈值以下,关联函数C均随交叉关联强度λ的增大而减小.在C-a₀曲线上存在单峰. 关键词： 单模激光 交叉关联 强度涨落 强度关联函数     

Normalized intensity correlation function of single-mode laser system driven by colored cross-correlation noises

Considering a single-mode laser system with cross-correlated additive colored noise and multiplicative colored noise, we study the effects of correlation among noises on the normalized intensity correlation function C(s).C(s) is derived by means of the projection operator method.     

Colored Gaussian noises induced stochastic resonance and stability transition for an insect growth system driven by a multiplicative periodic signal

In this paper, we focus on investigating the steady-state shift behaviors and the stochastic resonance phenomenon (SR) for a biological insect population system with a multiplicative periodic signal caused by the terms of the colored multiplicative and additive noises. Our research results imply that the multiplicative noise and the self-correlation of the additive noise can weaken the stability of the biological system and restrain the growth of the insect population, while the additive noise and the self-correlation time of the multiplicative noise can strengthen the stability of the insect system and facilitate the biological population to breed. As regards to the phenomenon of the SR evoked by a multiplicative periodic signal, noise terms and their correlation times, the computed results show that the additive noise intensity M and the self- correlation time τ₁ of the multiplicative noise can both improve the SR effect. Inversely, the multiplicative noise intensity Q and the self-correlation time τ₂ of the additive noise can suppress together the SR phenomenon. Whereas, it should be pointed out that in the SNR-Q and SNR-M plots, the two self-correlation times can both motivate a resonant peak, but not change the peak value of the SNR no matter how the two noise correlation times vary.     

Time dependence of entropy flux and entropy production for a dynamical system driven by noises with coloured cross-correlation

This paper shows the Fokker--Planck equation of a dynamical system driven by coloured cross-correlated white noises in the absence and presence of a small external force. Based on the Fokker--Planck equation and the definition of Shannon's information entropy, the time dependence of entropy flux and entropy production can be calculated. The present results can be used to explain the extremal behaviour of time dependence of entropy flux and entropy production in view of the dissipative parameter γ of the system, coloured cross-correlation time \tau and coloured cross-correlation strength \la.     

Noise-induced dynamics in a delayed bistable system with correlated noises

The resonance behaviors, such as coherence resonance and stochastic resonance, are studied in a delayed bistable system subject to correlated noises and a weak harmonic excitation. For weak noise intensities and small feedback gains, the analytic expressions of output spectrum and linear spectrum amplification are derived based on the theory proposed by Tsimring [14] [L.S. Tsimring, A. Pikovsky, Noise-induced dynamics in bistable systems with delay, Phys. Rev. Lett. 87 (2001) 250602]. The results show that the peak in the output spectrum at the frequency corresponding to the time delay attains the maximum for an intermediate amount of noise intensity and the coherence resonance appears. The correlation between noises can induce the suppression and the stochastic resonance in the curve of spectrum amplification, which is absent for the case of uncorrelated additive and multiplicative noises. Moreover, the system also exhibits the frequency stochastic resonance.     

Stochastic systems with cross-correlated Gaussian white noises

This paper theoretically investigates three stochastic systems with cross-correlation Gaussian white noises.Both steady state properties of the stochastic nonlinear systems and the nonequilibrium transitions induced by the cross-correlated noises are studied.The stationary solutions of the Fokker-Planck equation for three specific examples are analysed.It is shown explicitly that the cross-correlation of white noises can induce nonequilibrium transitions.     

周期混合信号和噪声联合激励下的非对称双稳系统的随机共振

研究了周期混合信号和关联的乘性和加性噪声联合激励下的非对称双稳系统的随机共振现象.运用两态理论,给出了基频和高阶谐频信噪比的理论结果.发现对于基频和高阶谐频情形下均出现随机共振，并且高阶谐频存在抑制现象.同时研究了非对称系数和噪声强度以及噪声之间关联强度对信噪比的影响.     

具有色关联的色噪声驱动下单模激光线性模型的随机共振

研究了具有指数形式关联的两色噪声驱动下单模激光线性模型受信号调制后其输出信噪比，发现了随机共振现象.根据计算结果讨论了噪声（即噪声强度、噪声间互关联程度和关联时间）和信号（信号频率和信号振幅）对信噪比的影响. 关键词： 随机共振 噪声关联时间 信噪比     

色噪声驱动的肿瘤细胞增长系统的瞬态性质:平均首通时间

研究了受色高斯噪声驱动的肿瘤细胞增长系统的瞬态态性质(平均首通时间T). 据Novikov定理和Fox近似方法得到相应的Fokker-Planck方程,使用最快下降法得到了肿瘤细胞增长系统的平均首通时间的解析表达式.经过数值计算,结果表明：肿瘤增长系统的T在正关联(0<λ<1, λ为关联噪声强度)和负关联(-1<λ<0)呈现出不同的特性. 正关联时,噪声强度和对应的关联时间在态转化过程中起着相反的作用;然而,负关联时,肿瘤增长系统的关键词： 色噪声 肿瘤细胞增长系统 平均首通时间     

Intensity correlation time of a single-mode laser driven by two coloured noises with coloured cross-correlation with direct signal modulation

In this paper, the intensity correlation time T is studied for the gain-noise model of a single-mode laser driven by coloured pump noise and coloured quantum noise with coloured cross-correlation with a direct signal modulation. By using the linear approximation method, it is found that when the pump noise is modulated directly by a signal, the effects of the cross-correlation between the pump noise and the quantum noise will disappear. In addition, there exists a maximum (i.e. resonance) in the curve of the intensity correlation time $T$ versus the pump noise self-correlation time \tau¹. Furthermore, when \tau¹\le\tau², the intensity correlation time T increases monotonically with the increase of $D$ and decreases monotonically with the increase of Q, but when \tau¹>\tau², the intensity correlation time T increases monotonically with the increase of Q and decreases monotonically with the increase of D.     

Current and efficiency enhancement in Brownian motors driven by non Gaussian noises

We study Brownian motors driven by colored non Gaussian noises, both in the overdamped regime and in the case with inertia, and analyze how the departure of the noise distribution from Gaussian behavior can affect its behavior. We analyze the problem from two alternative points of view: one oriented mainly to possible technological applications and the other more inspired in natural systems. In both cases we find an enhancement of current and efficiency due to the non-Gaussian character of the noise. We also discuss the possibility of observing an enhancement of the mass separation capability of the system when non-Gaussian noises are considered.Received: 8 July 2004, Published online: 30 September 2004PACS: 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.40.Jc Brownian motion - 87.16.Uv Active transport processes; ion channels     

Phase transitions in a bistable system driven by two colored noises

The colored noise problem is studied from the point of view of consistent Markovian approximations through extending unified colored-noise approximation to the case of two-colored-noise driving systems. A bistable system simultaneously driven by multiplicative and additive colored noise is investigated by means of the extended unified colored-noise approximation. It is found that, for weak strength and color of the additive noise, the form of the stationary probability distribution changes from a unimodal to a bimodal structure via a three modal one as the correlation time of the multiplicative colored noise increases, showing the system undergoes a first order phase transition from a monostable to a bistable state. Numerical simulations support our results. Received 10 August 1998 and Received in final form 23 April 1999     

Escape of Brownian particles in a bistable sawtooth potential driven by correlated white noises

An exact analytic expression of the relative escape rate (RER) for Brownian particles in a bistable sawtooth potential driven by correlated white noises is obtained. It is found that the RER vs. R (the multiplicative to the additive noise intensities ratio) exhibits a suppression platform for positive correlation, whereas the resonant activation and suppression platform appear successively for negative correlation. The mechanism of the present phenomena is explained. The effects of a nonlinear potential on the RER are studied. We have numerically calculated the RER of the system under a parabolic potential and a quartic potential and have compared the differences of the RER in the case of the linear potential and the one of the nonlinear potential. Received 16 September 2000 and Received in final form 15 January 2001     

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.     

色噪声激励下的FHN神经元系统

研究了色噪声激励下的FHN系统的相变问题和平均首次穿越时间,并推导了系统的定态概率密度函数和平均首次穿越时间表达式.结果表明,参数α,τ和β可以诱导相变,且存在锁定现象,各个参数对平均首次穿越时间都有很大影响,但影响效果有很大不同. 关键词： FHN系统 色噪声 平均首次穿越时间 定态概率密度     

Upper bound for the time derivative of entropy for a dynamical system driven by coloured cross-correlated white noises

It is shown how the cross-correlation time and strength of coloured cross-correlated white noises can set an upper bound for the time derivative of entropy in a nonequilibrium system. The value of upper bound can be calculated directly based on the Schwartz inequality principle and the Fokker--Planck equation of the dynamical system driven by coloured cross-correlated white noises. The present calculations can be used to interpret the interplay of the dissipative constant and cross-correlation time and strength of coloured cross-correlated white noises on the upper bound.     

Statistical properties of a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation for different correlation times

We study a system for a single-mode laser driven by additive and multiplicative coloured noises with a coloured cross-correlation. The analytical expression of the stationary intensity distribution (SID) for the laser is derived in the case of three different correlation times. The influences of each stochastic parameter on the SID are discussed, the effects of the noise "colour" and the cross-correlation of noises on the mean intensity , the variance, λ_2(0), and the skewness,λ_3(0) of the single-mode laser are investigated. We find that there are colourful phase transitions for the SID above a threshold, and re-entrant transitions induced by the "colour" of the additive noises. Further research of the curves of -τ_i, λ_2(0)-τ_i, and λ_3(0)-τ_i (i=1,2,3) (where τ_i is the correlation time) shows that the output intensity not only increases with the additive noise correlation time τ_2 and the cross-correlation time τ_3, but also the quality of the output of laser beams is optimized.