Effect of Correlated Noises in a Genetic Model

The Stratonovich stochastic differential equation is used to analyze genotype selection in the presence ot correlatecl Gaussian white noises. We study the steady state properties of the genotype selection and discuss the effects of the correlated noises. It is found that the degree of correlation of the noises can be used to select one type of genes from another type of mixing genes. The strong selection of genes caused by a large value of multiplicative noise intensity can be weakened by the intensive negative correlation.     

Correlated Noises of the Stochastic Processes

The combined effect of several noises has been proposed recently. It has displayed that the presence of the correlation between noises can change the properties of the stochastic processes. In this paper, a general effective Fokker-Planck equation (FPE) with correlated noises is derived. The stationary distributions and the moments of two kinetic models under two correlated noise sources are obtained. The effects of the interference of additive and multiplicative noises are analyzed.     

Extinction Time of a Metapopulation Driven by Colored Correlated Noises

The simplified incidence function model which is driven by the colored correlated noises is employed to investigate the extinction time of a metapopulation perturbed by environments. The approximate Fokker-Planck Equation and the mean first passage time which denotes the extinction time （Tex） are obtained by virtue of the Novikov theorem and the Fox approach. After introducing a noise intensity ratio and a dimensionless parameter R = D /α （D and a are the multiplicative and additive colored noise intensities respectively）, and then performing numerical computations, the results indicate that： （i） The absolute value of correlation strength A and its correlation time τ3 play opposite roles on the Tex; （ii） For the case of 0 〈λ〈 1,α and its correlation time τ2 play opposite roles on the Tex in which R〉 1 is the best condition, and there is one-peak structure on the Tex - D plot; （iii） For the case of-1 〈 λ≤ 0, D and its correlation time τ1 play opposite roles on the Tex in which R 〈 1 is the best condition and there is one-peak structure on the Tex - τ2 plot.     

Effect of Correlated Dichotomous Noises on Stochastic Resonance in a Linear System

A linear system driven by correlated asymmetric dichotomous noises and periodic signal was investigated in the overdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio (SNR) of the system were derived. By means of numerical calculations, we found that: (i) At some fixed multiplicative noise intensities, the output signal amplitude with frequency exhibits the structure of a weak peak, even no peak as the dichotomous noise is asymmetric; (ii) In the case of asymmetric dichotomous noise, the signal frequency can cause non-monotonous behavior of the output signal amplitude with respect to multiplicative noise intensity; (iii) The curve of SNR with frequency has a weak peak and a trough in the case of symmetric dichotomous noise, but no peak with asymmetric; (iv) Whether the multiplicative noise is symmetric or asymmetric, the noise can enhance response of the system; (v) The SNR increases with the correlation strength between the two noises decreasing. In addition, the plane of multiplicative noise intensity versus noise symmetric parameter was plotted.     

关联噪声对单模激光动力学性质的影响

应用线性近似方法,计算了具有指数形式关联的两白噪声驱动下的单模激光光强的关联函数、功率谱及关联时间。根据计算结果讨论了噪声间的关联程度和噪声间互联时间对以上各量的影响,并和噪声间具有δ函数关联形式的情况进行了比较     

System Driven by Correlated Gaussian Noises Related with Disorder

A system driven by correlated Gaussian noises related with disorder is investigated. The Fokker-Planck equation （FPE） for the system is derived. Using the FPE derived, some systems driven by correlated Gaussian noises related with disorder can be investigated for Brownian motors, nonequilibrium transition, resonant activation, stochastic resonance, and so on. We only give one example： i.e., using the FPE derived, we study the resonant activation for a single motor protein model with correlated noises related to disorder. Since the correlated noise related to disorder usually exists with the friction, for the temperature, and so on, our results have generic physical meanings for physics, chemistry, biology and other sciences.     

Stochastic Resonance in a Spatially Symmetric and Flashing Periodic Potential Subjected to Correlated Noises

A Brownian particle in a spatially symmetric and flashing periodic potential subjected to correlated noises is investigated. The exact expression of its current is analytically derived. The numerical results indicate that its current as a function of noise intensity exhibits two peaks in the case of positive correlations, and two vales in the case of negative correlations, i.e., a novel stochastic resonance （SR） phenomenon. The SR is attributed to the harmonic cooperation between the noises and the flashing periodic potential. The conditions under which the SR occurs are also presented.     

负关联噪声驱动下单模激光的定态分析

研究了负关联的加法和乘法高斯白噪声驱动下单模激光损失模型的定态情况。文中推导了负关联情况下，定态时的激光场幅的几率分布，光强的平均值，光强的协方差以及光强的偏斜率。并和文献〔１，２〕中正关联时的定态分析作了比较，发现了有意义的新现象。     

Intensity Correlation Function and Associated Relaxation Time of a Saturation Laser Model with Correlated Noises

We investigate the intensity correlation function C（s） and its associated relaxation time Tc for a saturation model of single-mode laser with correlated noises. The expressions of O（s） and Tc are derived by means of the projection operator method, and effects of correlations between an additive noise and a multiplicative noise are discussed by numerical calculation. Based on the calculated results, it is found that the correlation strength A between the additive noise and the multiplicative noise can enhance the fluctuation decay of the laser intensity.     

Probability and Joint Probability Distributions for Systems Driven by Correlated Colored Noises

This paper deals with systems driven by correlated colored noises. The evolution equations for both the single and joint probability distribution functions are derived. It is shown that both the stationary and dynamical properties of the systems are affected by correlated colored noises. These results are obtained by means of the systematic use of the ordered cumulant-expansion technique.     

Effects of Time Delay on the Bistable System Subjected to Correlated Noises

The time-delayed bistable system subjected to the multiplicative and additive noises is investigated. In the condition of small delay time, the stationary probability distribution function （SPDF） is derived, and under the condition of large delay time, the SPDF is stochastically simulated. The analytical and simulative results indicate that： （i） For the case of λ = 0 （λ denotes the strength of correlations between the multiplicative and additive noises）, the time delay affects weakly the SPDF peak structure, and the symmetrical property of the SPDF two-peak structure does not change with the increasing delay time. （ii） For the case of λ≠0, the two-peak structure changes with the increasing delay time, i.e. one peak goes up and the other go down simultaneously as the delay time increases and along with further increase of the delay time, the lower peak disappears gradually while the higher one goes up, i.e. the structure of the SPDF changes from a bimodal to a unimodal and the system becomes monostable.     

Escape of Brownian Particles in the System Driven by Correlated White Noises:Comparison of Three Models

The relative escape rate (RER) in the bistable sawtooth system driven by correlated white noises was studied in the case of linear multiplicative noise coefficient.And we compare the RER of linear multiplicative noise coefficient with the RER of the piecewise constant multiplicative noise coefficient in the bistable sawtooth system,finally compare the RER of the bistable sawtooth potential with the RER of the quartic potential in the case of linear multiplicative noise coefficient.It can be seen that the form of the multiplicative noise coefficient and the nonlinearity of potential have an important influence on the resonant activation and the suppression of the RER.The resonant activation of the RER vanishes in the negative correlation when the multiplicative noise coefficient was shifted from piecewise constant to linear function in the bistable sawtooth potential.The suppression of the RER disappears in the negative correlation when thelinear potential is converted into nonlinear one.``     

Escape of Brownian Particles in the System Driven by Correlated White Noises:Comparison of Three Models

The relative escape rate (RER) in the bistable sawtooth system driven by correlated white noises was studied in the case of linear multiplicative noise coefficient.And we compare the RER of linear multiplicative noise coefficient with the RER of the piecewise constant multiplicative noise coefficient in the bistable sawtooth system,finally compare the RER of the bistable sawtooth potential with the RER of the quartic potential in the case of linear multiplicative noise coefficient.It can be seen that the form of the multiplicative noise coefficient and the nonlinearity of potential have an important influence on the resonant activation and the suppression of the RER.The resonant activation of the RER vanishes in the negative correlation when the multiplicative noise coefficient was shifted from piecewise constant to linear function in the bistable sawtooth potential.The suppression of the RER disappears in the negative correlation when thelinear potential is converted into nonlinear one.     

Influence of Coloured Correlated Noises on Probability Distribution and Mean of Tumour Cell Number in the Logistic Growth Model

An approximate Fokker-Planck equation for the logistic growth model which is driven by coloured correlated noises is derived by applying the Novikov theorem and the Fox approximation. The steady-state probability distribution （SPD） and the mean of the tumour cell number are analysed. It is found that the SPD is the single extremum configuration when the degree of correlation between the multiplicative and additive noises, λ is in -1 〈λ≤0 and can be the double extrema in 0〈λ〈1. A configuration transition occurs because of the variation of noise parameters. A minimum appears in the curve of the mean of the steady-state tumour cell number, （x）, versus λ The position and the value of the minimum are controlled by the noise-correlated times.     

Correlated percolation in a film-deposition model

Clustering phenomenon has been studied in a film-deposition model in which a monolayer of particles is deposited onto a substrate. The occupation of a given site is assumed to depend on the occupation states of its nearest neighbouring sites as well as on the temperature of the particles being deposited. It is found that the percolating clusters remain ramified in that the number of their boundary sites are proportional to the number of particles in the cluster. The percolation threshold, however is lowered to (54±2)% as compared to 59% density for the uncorrelated case.     

Correlated migrations in a one-dimensional lattice

Particle migration in a one-dimensional lattice is treated in the presence of correlations between the directions of successive particle migrations.     

Correlated disorder in a Kondo lattice

Motivated by recent experiments on Yb-doped CeCoIn5, we study the effect of correlated disorder in a Kondo lattice. Correlations between the impurities are considered at the two-particle level. We use a mean-field theory approximation for the Anderson lattice model to calculate how the emergence of coherence in the Kondo lattice is impacted by correlations between impurities. We show that the rate at which disorder suppresses coherence temperature depends on the length of the impurity correlations. As the impurity concentration increases, we generally find that the suppression of coherence temperature is significantly reduced. The results are discussed in the context of available experimental data.     

Correlated electrons in a dissipative environment

When a system of correlated electrons is embedded in a dissipative environment, new emergent phenomena might occur due to the interplay of correlation and dissipation. Here we focus on quantum impurity systems with coupling to a bosonic bath. For the theoretical investigation we introduce the bosonic numerical renormalization group method which has been initially set up for the spin-boson model. The role of both correlations and dissipation is described in the context of two-electron transfer systems. We also discuss prospects for the investigation of lattice models of correlated electrons with coupling to a dissipative bath.