Can colored noise improve stochastic resonance?

The phenomenon of stochastic resonance is studied in the presence of colored noise. Several sources of colored noise are introduced and the consequences for the asymptotic time-periodic probability and the (phase-averaged) power spectrum are discussed. Based on space-time symmetry considerations, selection rules for the occurrence of-spikes in the power spectrum are derived. The effect of colored noise on the amplification of small periodic signals is studied in terms of effective, time-periodic Fokker-Planck equations: In overdamped systems driven by colored noise, we find that SR is suppressed with increasing noise color. In contrast, for colored noise induced by inertia (as well as for asymmetric dichotomic noise), one obtains an enhancement of SR. This latter result is obtained by studying the Kramers equation perturbed by a small periodic force.     

Transient Properties of One-Dimensional Stochastic Processes: Unified-Colored-Noise Approximation

By virtue of the unified-colored-noise approximation the formulas of mean, variance and skewness of first-passage-time distributions (FPTD) for the systems driven by colored noise are derived. The mean and variance of FPTD of bistable system driven by colored noise are calculated. The approximation expressions of the mean, variance and skewness of FPTD for the colored cubic model of a dye laser are obtained. The role of the "color" of pump noise in the dye laser transient is analyzed.     

Path integral solutions for non-Markovian processes

For a nonlinear stochastic flow driven by Markovian or non-Markovian colored noise (t) we present the path integral solution for the single-event probabilityp(x,t). The solution has the structure of a complex-valued double path integral. Explicit formulas for the action functional, i.e., the non-Markovian Onsager-Machlup functional, are derived for the case that (t) is characterized by a stationary Gaussian process. Moreover, we derive explicit results for (generalized) Poissonian colored shot noise (t). The use of the path integral solution is elucidated by a weak noise analysis of the WKB-type. As a simple application, we consider stochastic bistability driven by colored noise with an extremely long correlation time.     

Inertial effects of a small Brownian particle cause a colored power spectral density of thermal noise

The random thermal force acting on Brownian particles is often approximated in Langevin models by a "white-noise" process. However, fluid entrainment results in a frequency dependence of this thermal force giving it a "color." While theoretically well understood, direct experimental evidence for this colored nature of the noise term and how it is influenced by a nearby wall is lacking. Here, we directly measured the color of the thermal noise intensity by tracking a particle strongly confined in an ultrastable optical trap. All our measurements are in quantitative agreement with the theoretical predictions. Since Brownian motion is important for microscopic, in particular, biological systems, the colored nature of the noise and its distance dependence to nearby objects need to be accounted for and may even be utilized for advanced sensor applications.     

Spin relaxation. The renormalized operator cumulant approach

Two-level systems under the influence of external noise are generic models of quantum relaxation processes. The spin 1/2 particle in a stochastic magnetic field is one of the best known examples. Interesting effects are observed if the noise is colored as is the case in most applications. The time-ordered operator cumulant expansion forms a convenient approach to this problem. Recently, a renormalization procedure has been proposed which corresponds to a partial summation of the naive expansion and hence constitutes an essential improvement over the second cumulant considered usually. For colored noise of intermediate strength and correlation time this approach is used to derive renormalized expressions for the transverse (T ₂) and longitudinal (T ₁) relaxation time and the frequency shift. In this parameter region, the ratioT ₁/T ₂= is found to deviate substantially from its value =2 valid for white noise exactly and for colored noise in the second cumulant approximation. This corroborates and extends results of Budimir and Skinner obtained by including the second and fourth cumulant only. However, their truncated expansion is shown to lead to unphysical results in the intermediate parameter region treated still correctly by the renormalized expansion.     

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.     

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.     

Colored multiplicative and additive non-Gaussian noise-driven dynamical system: Mean first passage time

We have studied the barrier crossing dynamics in presence of non-Gaussian noises. It has been observed that multiplicative colored non-Gaussian noise can induce resonant activation (RA). The conspicuous dependence of mean first passage time (MFPT) on correlation time (_τ2${\tau }_2$) of additive colored noise having fixed variance have been analyzed. Beyond a critical value of _τ2${\tau }_2$ the MFPT increases for a given rate of increase of noise strength with _τ2${\tau }_2$ if the additive colored noise is non-Gaussian. The MFPT first decreases with increase of the non-Gaussian parameter (measures deviation from Gaussian character) of multiplicative colored noise followed by an increase exhibiting a minimum. The appearance of the minimum critically depends on the additive noise.     

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.     

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.     

Mode competition Effects of a Two Mode Laser with Multiplicative Colored Noise

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Stochastic calculus in physics

The relationship of the Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the Ito-Stratonovich calculus for white noise. It also provides an approach to steady state behavior for strongly colored noise. Numerical simulation algorithms are explored, and a novel suggestion is made for efficient and accurate simulation of white noise equations.     

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     

Influence of Delayed-Time and Colored-Noise in a Bistable System Subject to Asymmetric Dichotomous Noise and Colored Noise

The influence of delayed-time and colored-noise in a bistable system subject to asymmetric dichotomous noise and colored noise is studied. Applying small delay-time approximation, under the adiabatic limit condition, the expression of the signal-to-noise ratio (SNR) of the system is obtained. It is found that, the SNR varies non-monotonously with the delayed-time and the correlation of the colored noise. Moreover, the SNR exhibits SR behavior when it is plotted as a function of the intensity and asymmetry of the dichotomous noise, and as a function of the strength of the colored noise.     

基于CCF-TLS-ESPRIT算法的低频振荡在线辨识

低频振荡在线辨识需用到广域测量系统(WAMS)的采集信号,而WAMS采集的信号中常伴有高斯白噪声,经过常规的低通滤波处理后会产生高斯色噪声,从而影响辨识的精度.针对在线辨识中的色噪声问题,提出以互相关函数(CCF)来代替实测信号,从而抑制色噪声,并结合总体最小二乘-旋转不变技术参数估计(TLS-ESPRIT)算法进行模态辨识.仿真结果表明,CCF-TLS-ESPRIT算法能够有效辨识出色噪声环境中的系统低频振荡模态,并具有一定的效率.     

色噪声对光学双稳态的影响

采用统一色噪声近似构建了由乘法色噪声驱动的纯吸收型光学双稳态状态方程,并分析了色噪声对光学双稳态的影响,将结果与白噪声驱动的光学双稳态进行比较.结果表明:当乘法噪声与加法噪声处在正关联时,增加乘法色噪声的自关联时间r,光学双稳性的区域显著变宽,即磁滞回线面积变大;当乘法噪声与加法噪声处在负关联时,只有乘法噪声较小时,改变乘法色噪声的自关联时间r,光学双稳态才发生改变;当乘法噪声的自相关时间等于零时,本文模型退化为乘法白噪声驱动的光学双稳性状态方程.     

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。     

Dynamical Properties of a Single-Mode Laser with Both Colored Noise and Injected Signal

The colored noise in a single-mode laser with injected signal is investigated by the method of two-dimensional unified colored noise approximation. The normalized correlation function λ₂(0), the intensity correlation time T_c and effective eigenvalue λ_eff are calculated. The effects of the injected signal I₀, colored noise strength P^ˊ and the noise correlation time τ on the dynamical properties of the single-mode laser are discussed.     

Array-enhanced logical stochastic resonance subject to colored noise

This paper proposes an approach that uses a parallel array to improve the reliability and robustness of logical stochastic resonance subject to colored noise. The experimental results demonstrate that (i) the increase of array size can extend the optimal range of noise intensity and increase the maximum probability of obtaining correct logic operation. (ii) The optimal range of noise correlation time is broadened with the increase of array size. (iii) The main difference between logical stochastic resonance subject to white noise and colored noise is that the increase of noise correlation time broadens the optimal range of noise intensity when the stochastic noise is colored noise. At the same time, the maximum probability of obtaining correct logic operation is close to 1. Therefore, reliable and robust logic gate can be realized under a certain array size.