色关联的色噪声驱动的分段非线性模型的平均首次穿越时间

研究了色关联的乘性高斯色噪声和加性高斯色噪声驱动的分段非线性系统中, 噪声强度和相关时间对平均首次穿越时间的影响. 利用一致有色噪声近似方法和最速下降方法, 推导出系统平均首次穿越时间的表达式. 研究结果表明: 系统的平均首次穿越时间随着乘性噪声的增加会出现单峰结构, 即“共振”现象, 峰值会随着加性噪声强度和噪声之间关联强度的增加而减小. 而平均首次穿越时间作为加性噪声的函数呈单调曲线, 说明乘性噪声和加性噪声对平均首次穿越时间的影响不同. 此外, 乘性和加性噪声关联时间以及互关联时间在正关联时和负关联时 对系统平均首次穿越时间的影响是不同的. 关键词： 色噪声 分段非线性系统 平均首次穿越时间     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Colored Noise in First-order-like Phase Transition of a Laser System

The decoupling theory is employed to analyze the multiplicative colored noise in a single mode laser system. Steady state intensity distribution function is derived when colored noise is included in the laser system. The first-order-like phase transition driven by multiplicative colored noise is investigated and compared with the case of multiplicative white noise. It is shown that the noise correlation time can affect the parameter plane of the first-order-like phase transition. The steady state intensity distributions in a laser system is changed greatly with noise correlation time τ.     

Structure changes induced by external multiplicative noise in the electrohydrodynamic instability of nematic liquid crystals

We study the influence of external multiplicative noise on the electrohydrodynamic instability (EHD) in nematic liquid crystals. It turns out that the correlation time _n and the intensityQ of the noise are the crucial parameters to control the system. Different types of noise lead to minor quantitative changes when compared to Gaussian white noise, leaving the qualitative aspects unchanged. With increasing noise intensity the threshold for the onset of the first instability changes drastically. We observe that the curvature arising when the threshold of the various instabilities is plotted as a function of the noise intensity changes as one is going, e.g., from the onset of Williams domains (WD) to the onset of the grid pattern (GP). This result reflects the transition in the flow structure from two-dimensional (WD) to three-dimensional (GP, DSM) flow patterns. As the intensity of the noise is increased further, the onset of the first instability becomes more complex. The measurement of the nonlinear onset time shows a strong dependence on the noise intensityQ, which is linear for WD and GP well above onset. The linear onset time shows an unexpected dependence on the noise intensity close to the onset of the first instability. For sufficiently long correlation times of the noise, a destabilization by noise is obtained.     

色高斯噪声驱动双稳系统的多重随机共振研究

研究了由色关联乘性和加性色噪声作用下的双稳系统的随机共振问题,在绝热近似条件下得到了信噪比的表达式.通过分析所得的初始条件为 x(0)=x₊ 时的信噪比,发现了单随机共振和多重随机共振现象;分析了噪声强度、噪声关联时间和关联强度对系统信噪比的影响. 关键词： 多重随机共振 信噪比 双稳模型 色关联色噪声     

A new method of analysis of the effect of weak colored noise in nonlinear dynamical systems

A systematic method for obtaining the asymptotic behavior of a dynamical system forced by colored noise in the limit of small intensity is developed. It is based on the search of WKB solutions to the Fokker-Planck equation for the joint probability density of the system and noise, in which the perturbation expansion is continued to the first correction beyond the Hamilton-Jacobi limit. The method can be applied to noise with correlation time of order unity. It is illustrated on the normal form of a pitchfork bifurcation, where it is pointed out that additive noise can induce a shift of the most probable value. This prediction is confirmed by numerical simulation of the stochastic differential equations.     

染料激光色立方模型定态性质的描述

应用一般形式的统一色噪声近似得到了洒料激光色立方模型光强分布的福克－普朗克方程。导出了光强分布函数，描述了光强涨落的实验和数值模拟结果以及色噪声对光强涨落的影响。     

Moments and Mean First—Passage Time of Parabolic—Bistable Potential System Driven by Colored Noise

A parabolic-bistable potential system driven by colored noise is studied.The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived.Furthermore,the mean first-passage time is calculated by the use of two approximate methods,respectively.It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity;(ii) a minimum occurs on the curve of the second-order moment of the system vs.noise intensity at the point DΓ=0.025;(iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time τ,while the conventional steepest descent approximation leads to poor results.     

Nano-friction phenomenon of Frenkel—Kontorova model under Gaussian colored noise

The nano-friction phenomenon in a one-dimensional Frenkel-Kontorova (FK) model under Gaussian colored noise is investigated by using the molecular dynamic simulation method. The role of colored noise is analyzed through the inclusion of a stochastic force via a Langevin molecular dynamics method. Via the stochastic Runge-Kutta algorithm, the relationship between different parameter values of the Gaussian colored noise (the noise intensity and the correlation time) and the nano-friction phenomena such as hysteresis, the maximum static friction force is separately studied here. Similar results are obtained from the two geometrically opposed ideal cases: incommensurate and commensurate interfaces. It was found that the noise strongly influences the hysteresis and maximum static friction force and with an appropriate external driving force, the introduction of noise can accelerate the motion of the system, making the atoms escape from the substrate potential well more easily. Interestingly, suitable correlation time and noise intensity give rise to super-lubricity. It is noteworthy that the difference between the two circumstances lies in the fact that the effect of the noise is much stronger on triggering the motion of the FK model for the commensurate interface than that for the incommensurate interface.     

Effects of colored noise on the dynamics of quantum entanglement of a one-parameter qubit—qutrit system

We analyzed the effect of colored noise on the negativity dynamics of a hybrid system consisting of a qubit-qutrit and not interacting, prepared from the start in an entangled one-parameter state and acting with noise in local and non-local environments. In this pink and brown noise we investigated two different situations: in the first situation, the noise is produced by a bistable oscillator with an unknown exchange rate; however, in the second situation, the noise is generated by a set of bistable oscillators. We found that entanglement decreases with time to zero, and undergoes the phenomenon of sudden death and rebirth. The pink noise is more prone to entanglement than the brown noise and the non-local environment is more prone to entanglement than the local one. When the number of fluctuators is increased, entanglement decays faster and finally, for certain parameters of the initial state, the subsystems are not affected by the noise.     

Fluctuations of Single-Mode Laser Driven by Two Different Kinds of Colored Noise

A single-mode laser with coupling between additive and multiplicative noise terms is investigated when the multiplicative noise and the coupling between two noise terms are colored fluctuations with finite correlation times T1 and τ2. Combining the unified colored noise approximation (UCNA) and the functional analysis, the stationary probability distribution (SPD) and the variance of the laser intensity is derived. It is found that the colored nature of multiplicative noise and the coupling strength between two noise terms can affect both the structure and the height of the SPD, while the colored nature of the coupling between two noise terms can only affect the height of the SPD. The multiplicative noise can enhance the intensity fluctuations while the additive noise can reduce the fluctuations in a laser system. Numerical simulations are presented and consistent to the analytical results.     

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance （SR） in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio （SNR） is calculated according to the generalized two-state theory （shown in [H.S. Wio and S. Bouzat, Brazilian J.Phys. 29 （1999） 136]）. We find that the SNR increases with the proximity of a to zero. In addition, the correlation time T between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time T between the Gaussian additive colored noise is, the higher of the peak value of SNR.     

色关联乘性和加性色噪声驱动的多稳态系统的稳态特性

研究了色关联乘性和加性色噪声作用下的三稳态系统的稳态问题.首先利用一致有色噪声近似方法,推导出稳态概率密度函数的表达式,然后分析了乘性噪声和加性噪声的强度以及关联性对稳态概率密度函数的影响,研究结果表明:加性噪声强度、加性噪声和乘性噪声的关联强度和关联时间可以诱导系统的非平衡相变.     

偏置信号调制下噪声关联的周期调制对单模激光随机共振的影响

在噪声受偏置信号调制的情况下,讨论色噪声之间的关联受时间周期调制所驱动的单模激光系统中的随机共振.用线性化近似的方法计算了输出信噪比.具体讨论输出信噪比随噪声自关联时间、噪声强度和偏置信号的变化关系.发现输出信噪比随抽运噪声强度和自关联时间的变化出现随机共振,而偏置信号会降低随机共振的峰值.实际应用中应控制优选偏置信号强度. 关键词： 偏置信号 色噪声 时间周期调制 噪声间关联程度     

色交叉关联噪声作用下集合种群的稳定性和平均灭绝时间

在Levins模型的基础上研究了色交叉关联噪声对集合种群稳定性的影响, 应用Fokker-Plank方程得到了系统的稳态概率密度函数, 运用最快下降法得到了平均灭绝时间的解析式. 结果表明: 两噪声色关联时, 加性噪声强度和乘性噪声强度均弱化集合种群的稳定性; 噪声关联强度强化集合种群的稳定性. 两噪声之间负关联时, 平均灭绝时间是加性噪声强度和乘性噪声强度的减函数, 是噪声关联时间的增函数; 两噪声之间正关联时, 平均灭绝时间是加性噪声强度和噪声关联时间乘性噪声强度的减函数, 是乘性噪声强度的非单调函数. 关键词： 集合种群 色交叉关联噪声 稳定性 平均灭绝时间     

相干介观系统中散粒噪声的Monte Carlo模拟方法研究

根据电荷通过低温量子导体时具有的二项分布导致散粒噪声这一结论,结合Landauer电流公式的物理内涵建立了相干介观系统中的散粒噪声模型,并通过Monte Carlo模拟方法产生了散粒噪声时间序列.介观系统中散粒噪声的抑制来源于电子输运时的相关性,传输本征值双峰分布导致量子混沌腔和无序金属中的散粒噪声抑制.根据这两个结论,通过Monte Carlo模拟定性地分析了传输本征值分布与电子输运相关性之间的关系. 关键词： 散粒噪声 Landauer公式 介观系统     

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}     

Systems Driven by Colored Poisson Noise: Unified Colored Noise Approximation

In this paper, unified colored noise approximation is extended to treat the systems driven by Poisson colored noise χ = ν(χ) + gε_cp(t). We arrive the evolution equation of the probability distribution pi(x, r) and the stationary probability distribution pt (χ, Υ). These equations are valid only if γ(χ,Υ) ≡ γ^-1/2[1 - ΥG(χ)/g(χ)] (G(χ) ≡ v'(χ)g(χ) - v(g)g'(χ)) is large enough (positive) and t >> Υ/γ(χ, Υ), but Υ is not restricted. As an application, we derive the nonlinear relaxation time (NLRT) for the processes driven by Poisson colored noise and evduate the NLRT for the approximative Ginzburg-Landon model under small Υ.     

Steady-State Analysis of a Single-Mode Laser Driven by Colored Pump Noise with Cross-Correlation Between Real and Imaginary Parts of Quantum Noise

Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λq between the real and imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Qst(I), the mean (I）, and the variance λ2(0) of the laser intensity. It is shown that cross-correlation intensity λq of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠0), improving the pump parameters monotonously will make the curves of Qst(I) exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λq and τ when the laser is operated near or below threshold. Especially when τ≠0, the heights of the peaks of the curves of λ2(0)-α0 and α3(0)-α0, (here a0 is the net gain coefficient) go up as λq increases. However the entire curves λ2(0)-α0 and λ3(0)-α0 are abruptly suppressed when λq = 1, in similarity to phase transition of stationary intensity distribution.     

Effect of external fluctuations on the Fréedericksz transition in an analogue simulator

The influence of multiplicative external fluctuations (noise) on the phenomenological equation describing the Fréedericksz transition has been studied by means of an electronic analogue simulator. Measurements were made of the stationary probability density for a wide range of fluctuation intensities and correlation times, for both dichotomous and Gaussianly distributed noise. For dichotomous forcing, the resultant phase diagrams at particular values of the field intensity parameter were found to be in satisfactory agreement with exact theoretical predictions by Horsthemkeet al. In the (physically more realistic) case of Gaussian fluctuations, for which no theory is currently available, the results obtained were distinctively different. A physically motivated discussion is given to account for the interesting differences and similarities of behavior found for the two types of external noise.