Genotype selection model with two time-correlated white noises

We study the steady state properties of a genotype selection model in the presence of two time correlated Gaussian white noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution has been investigated. The fluctuation of both the mutation factor and the genetic factor can break the balance of the gene selection. The fluctuation of the genetic factor can facilitate the gene separation which allows us to select one gene-type haploid from a gene group while the fluctuation of the mutation factor impedes the gene separation. Remarkably, the correlation time between the two noises can induce the system to change from two states to one.     

随机基因选择模型中的延迟效应

研究了噪声驱动的基因选择模型中的延迟效应. 据小延迟方法和随机等价法则得到相应的延迟Fokker-Planck方程, 给出稳态概率分布函数的近似表达式. 分析了在噪声驱动下, 延迟时间对系统稳态性质的影响. 结果表明: 延迟时间可以诱导系统从单稳态向双稳态转化, 发生相变; 在基因选择过程中, 延迟时间有利于从基因群体中选择出某一单倍体基因. 数值模拟结果与理论预测基本符合.     

Noise in Genotype Selection Model

We study the steady state properties ofa genotype selection model in presence of correlated Gaussian whitenoise. The effect of the noise on the genotype selection model is discussed. It is found that correlated noise can breakthe balance of gene selection and induce the phase transition which can makes us select one type gene haploid from agene group.     

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.     

Correlated noises in an absorptive optical bistable model

We study the steady state properties of an absorptive optical bistable model in the presence of correlated noises. Based on the corresponding Fokker-Planck equation the steady state solution of the probability distribution and the average value of the transmitted light have been investigated. We have found that fluctuations of the input light amplitude improve the transmitted light and an optimized value exists for the fluctuations of the population difference at which the transmitted light takes its maximum value. The correlation between the two noises reduce the transmitted light and the noises in the model can induce a phase transition.     

Escape of Brownian particles in an asymmetric bistable sawtooth potential driven by cross-correlated noises

The relative escape rate (RER) for Brownian particles in an asymmetric bistable sawtooth potential driven by cross correlations between multiplicative white noise and additive white noise is studied. A new expression of the mean first-passage time is derived under the condition of piecewise linear potentials and discontinuous diffusion function. Based on the results of RER numerically calculated, it is found that (i) under positively correlated noises action (i.e. λ > 0, and λ is the correlation strength), the escape rate exhibits the suppression platform as the intensity of multiplicative noise varies. The effect of suppression becomes more pronounced with the growth of height of the deterministic potential barrier for transition, and with the increase of λ. However, for the case of uncorrelated noises (λ = 0) and of negatively correlated noises (λ < 0), the suppression platform disappears. (ii) The positive correlation between noises amplifies the change of the escape rate with the height of barrier for transition, while the negative correlation between noises suppresses this change. Received 20 November 2002 / Received in final form 19 October 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: kmdcmei@public.km.yn.cn     

Micro-transitions or breathers in L-alanine?

Within mean field approximation, a procedure is elaborated to consider noise induced phase transitions with arbitrary relations between the noises of different degrees of freedom. The proposed approach is applied to investigate effects of cross correlation between noises in the generalized synergetic model of Lorenz type. This cross correlation is shown to induce phase transitions of the dynamical system under consideration. Additionally, we find the correlation between noises transforms a synergetic behavior to a thermodynamic one. Received 13 November 2002 Published online 11 April 2003 RID="a" ID="a"e-mail: dikh@sumdu.edu.ua     

SUPERCONDUCTING JUNCTIONS IN THE CASE OF CORRELATED SYMMETRIC NOISES

We study two models for Josephson junctions, i.e.,a Gaussian white noise model and a symmetric dichotomous noises model. In this study we find that the correlated symmetric noises can produce a net voltage. This phenomenon is due to the correlation between the additive and the multiplicative noises. We show some characteristic features for this phenomenon: the net voltage is always negative and has a peak value when the strength of the additive noises varies for the former model(or when the strengths of the noises vary for the latter model). The results provide a theoretical foundation for reducing the net voltage caused by the correlated symmetric noises.     

Additive Temporal Coloured Noise Induced Eckhaus Instability in Complex Ginzburg-Landau Equation System

The effect of additive coloured noises, which are correlated in time, on one-dimensional travelling waves in the complex Ginzburg-Landau equation is studied by numerical simulations. We found that a small coloured noise with temporal correlation could considerably influence the stability of one-dimensional wave trains. There exists an optimal temporal correlation of noise where travelling waves are the most vulnerable. To elucidate the phenomena, we statistically calculated the convective velocities Vg of the wave packets, and found that the coloured noise with an appropriate temporal correlation can decrease Vg, making the system convectively more unstable.     

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.     

噪音关联对单模激光光强定态几率分布的影响

从理论上对加性白噪音和乘性色噪音之间存在关联作用的单模激光立方模型进行了分析.通过数值计算得到;噪音关联时间和噪音关联强度参量对光强定态几率分布曲线有很大影响;特别地,当两噪音之间存在完全负关联时,光强被锁定在某一固定值处.     

Effects of the Noise on Voltage-Current Characteristics of Josephson Effect

In the case of T >> hω/k, by expanding the quasiparticle current power spectrum up to the third order term of hω/2kT, two noises are obtained: one is a white noise, the other is an O-U noise. We find that the two noises are the negative correlated noises, and correlation parameter λ is equal to -√6/3. Effects of the correlated noises on voltage-current characteristics curve are studied. The numerical computations show that the correlation parameter λ has very large effects on the voltage-current characteristics, but the correlation time τ of the O-U noise has a little effect.     

单模激光系统随机共振的模拟研究

用数值模拟方法对具有调制信号的单模激光系统进行了研究, 分析了在阈值附近和远离阈值两种工作方式下的输出信噪比、输出信号功率、 背景噪声功率,并与线性化近似结果进行了对比. 研究发现,激光在阈值附近工作时,输出信噪比会随着量子 噪声的增大出现随机共振现象,这一现象不要求泵噪声与量子噪 声存在关联,但噪声之间的关联会进一步增大信噪比;在远离阈值时, 只有噪声间存在关联时才会发生随机共振现象.研究还发现噪声也 会影响输出信号的功率.     

Stochastic resonance of bias signal-modulated noise in a single-mode laser＊

Stochastic resonance (SR) for bias signal modulation is studied in a single-mode laser system. By investigating a gain-noise model driven by correlated pump noise and quantum noise, we find that, whether the correlation coefficient between both the noises is positive or negative, SR always appears in the dependence of signal-to-noise ratio (SNR) upon the noise correlation time and the frequency of the modulation signal. However, only when the correlation coefficient between both noises is negative can SR occur in the dependence of SNR upon the quantum noise intensity and pump noise intensity, while when the correlation coefficient between both noises is positive, it shows monotonically.     

Effects of cross-correlated noises on the relaxation time of the bistable system

The stationary correlation function and the associated relaxation time for a general system driven by cross-correlated white noises are derived, by virtue of a Stratonovich-like ansatz. The effects of correlated noises on the relaxation time of a bistable kinetic model coupled to an additive and a multiplicative white noises are studied. It is proved that for small fluctuations the relaxation time T_c as a function of λ (the correlated intensity between noises) exhibits very different behaviours for αD (α and D, respectively, stand for the ntensities of additive and multiplicative noises). When α>D, T_c increases with increasing λ. But when α相似文献   

Intensity correlation function of an optical bistable system subjected to cross-correlated noises

The normalized correlation function C(s) of an optical bistable system driven by cross-correlated noises is investigated. Based on the numerical computation and simulation results, it is found that: (1) The intensity of multiplicative noise D and the intensity of additive noise Q play opposite roles on C(s), i.e., D enhances the rate of fluctuation decay of transmitted light intensity and Q slows down the rate of fluctuation decay of the transmitted light intensity; (2) The strength of correlations between the multiplicative and additive noises λ slows down the rate of decay of intensity fluctuation; (3) For the case of positive correlated noises (λ>0), the increasing cooperativity parameter C slows down the rate of decay of intensity fluctuation firstly and then enhances it; (4) For the case of negative correlated noises (λ<0), the increasing C almost does not affect the rate of decay of intensity fluctuation firstly and then enhances it.     

Effect of correlated noises on Brownian motor

The Brownian motor operating between two correlated Gaussian white noises was investigated. The expressions of the current and the energy conversion efficiency of the Brownian motor were analytically derived by exploiting adiabatic approximation. The results indicates that: (i) Regulating the correlation strength λ between the two noises and the ratio D₂/D₁ of the two noise intensities can change the rotational direction of the motor; (ii) For the smaller D₂/D₁, an optimal λ can make the positive current and the efficiency be maximal, and for the smaller λ, an optimal D₂/D₁ also let the positive current be maximal. The results were explained from a viewpoint of modified potentials. The study is of important significance in the aspect of controlling the operation of the Brownian motor.     

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.     

乘性噪音和加性噪音效应对脉孢菌生物钟体系内信号随机共振的增强

利用有和无外信号作用的脉孢菌生物钟体系,研究了与加性噪音相关或不相关的乘性噪音对加性噪音诱导出的内信号随机共振的影响作用.结果表明：无外信号的情况下,不论加性和乘性噪音相关与否,当乘性噪音强度小于临界值时,乘性噪音的加入使加性噪音诱导产生的内随机共振强度得到增强;当大于其临界值时,加性噪音的随机共振强度却得不到进一步增强,这说明脉孢菌生物钟体系能抵抗外噪音的干扰而维持自身的生理节奏.当加入外信号时,对于乘性和加性噪音不相关的情况,发现存在最佳频率（0.003 Hz）的外信号能使加性噪音诱导出的内信号随机共 关键词： 噪音 脉孢菌生物钟体系 内信号随机共振     

Efficiency and current in a correlated ratchet

We present a detailed study of the transport and the efficiency of a ratchet system in a periodic potential in the presence of correlated noises. The current and the efficiency of the system are investigated. It is found that, when the potential is spatially symmetric, the correlation between the two noises can induce a net transport. The efficiency shows many interesting features as a function of the applied force, the noise intensity, the external load, etc. The efficiency can be maximized as a function of noise intensity (or temperature), which shows that the thermal fluctuation can facilitate the efficiency of energy transformation.