Brownian motors: Joint effect of non-Gaussian noise and time asymmetric forcing

Previous works have shown that time asymmetric forcing on the one hand, as well as non-Gaussian noises on the other, can separately enhance the efficiency and current of a Brownian motor. Here, we study the result of subjecting a Brownian motor to both effects simultaneously. Our results have been compared with those obtained for the Gaussian white noise regime in the adiabatic limit. We find that, although the inclusion of the time asymmetry parameter increases the efficiency value up to a certain extent, for the present case this increase is much less appreciable than in the white noise case. We also present a comparative study of the transport coherence in the context of colored noise. Though the efficiency in some cases becomes higher for the non-Gaussian case, the Péclet number is always higher in the Gaussian colored noise case than in the white noise as well as non-Gaussian colored noise cases.     

Stationary properties of a single-mode laser system with non-Gaussian and Gaussian noise

A single-mode laser system with non-Gaussian and Gaussian noise is investigated. The stationary mean value and the normalized variance of the laser intensity are numerically calculated under the condition that the stationary probability distribution function (SPDF) is derived. The SPDF as a function of the laser intensity exhibits a maximum. The maximum becomes smaller with the increase of the correlation intensity or the non-Gaussian parameter, where the later is a measure of the deviation from the Gaussian characteristic. The maximum becomes larger as the correlation time increases. The laser intensity stationary mean value decreases with the increase of the correlation intensity or the non-Gaussian parameter while increases with the correlation time increasing. The laser intensity normalized variance increases with the increase of the correlation intensity or the non-Gaussian parameter while decreases as the correlation time increases.     

Effects of colored noise and noise delay on a calcium oscillation system

As a calcium oscillations system is in steady state, the effects of colored noise and noise delay on the system is investigated using stochastic simulation methods. The results indicate that: (1) the colored noise can induce coherence bi-resonance phenomenon. (2) there exist three peaks in the R–_τ0$R\text{–}{\tau }_0$ (R$R$ is the reciprocal coefficient of variance, and _τ0${\tau }_0$ is the self-correlation time of the colored noise) curves. For the same noise intensity Q=1$Q=1$, the Gaussian colored noise can induce calcium spikes but the white noise cannot do this. (3) the delay time can improve noise induced spikes regularity as _τ0${\tau }_0$ is small, and R$R$ has a significant minimum with increasing τ$\tau$ as _τ0${\tau }_0$ is large. (4) large values of ζ$\zeta$ reduce noise induced spikes regularity.     

Stochastic properties of tumor growth with coupling between non-Gaussian and Gaussian noise terms

Dynamical behavior of tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect.     

Stochastic properties coupling between of tumor growth with non-Gaussian and Gaussian noise terms

Dynamical behavior of a tumor-growth model with coupling between non-Gaussian and Gaussian noise terms is investigated. The departure from the Gaussian noise can not only reduce the probability of tumor cells in the active state, induce the minimum of the average tumor-cell population to move toward a smaller non-Gaussian noise, but also decrease the mean first-passage time. The increase of white-noise intensity can increase the tumor-cell population and shorten the mean first-passage time, while the coupling strength between noise terms has opposite effects, and the noise correlation time has a very small effect.     

The study on a stochastic system with non-Gaussian noise and Gaussian colored noise

In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker-Planck equation, and the expressions of stationary probability density function and mean first-passage time are presented. Also we explore the effects of correlation between non-Gaussian and Gaussian noise for the mean first-passage time.     

Effects of non-Gaussian noise on a calcium oscillation system

We investigate the effects of the non-Gaussian colored noise on a calcium oscillation system using stochastic simulation methods. It is found that the reciprocal coefficient of variance R has a maximum (R max ) with increasing noise intensity Q. The non-Gaussian noise parameter q has an important effect on the system. For some values of q (e.g., q = 0.9, q = 1.0), R has a maximum with increasing correlation time τ. Non-Gaussian noise induced spikes are more regular than Gaussian noise induced spikes when q is small and Q has large values. The R has a maximum with increasing q. Therefore, non-Gaussian noise could play more effective roles in the calcium oscillation system.     

Effects of non-Gaussian noise on the dynamical properties of a logistic system

The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non- Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q 〉 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.     

非高斯噪声对惯性棘轮中粒子负迁移率的影响

利用随机模拟方法研究了惯性棘轮中非高斯噪声对负迁移率的影响. 分别模拟了绝对负迁移率(ANM), 非线性迁移率(NNM) 和负微分迁移率(NDM) 等三种反常输运现象. 计算结果表明: 1) 在不同的参数空间里, 非高斯噪声参数q 能够增强或者削弱ANM, 诱导NNM 和NDM; 2) 当q 较大时, 反常输运现象转化为正常输运; 3) 随着q 逐渐增大, 平均速度- 关联时间特性曲线朝着关联时间较小的方向移动并且其峰值逐渐减小. 关键词： 反常输运 负迁移率 非高斯噪声     

Effects of time delay and non-Gaussian noise on the dynamics of a perceptual bistability

In this paper, we investigate the effects of time delay and non-Gaussian noise on the dynamics properties of the attractor network model of perceptual bistability. Using delay Fokker–Planck equation and projection operator method, the stationary probability distribution P_st(x), the associated relaxation time T_c, and the normalized correlation function C(s) for perceptual bistability are obtained, respectively. Research results show that: (i) the time delay τ and the correlation time τ₀ from non-Gaussian noise can induce the change of the peaks in the P_st(x), i.e., the transition of the system appears; (ii) there exhibits an optimal value of the τ₀ or τ by which the T_c or C(s) is maximum, this maximum shows the τ₀ or τ first reduces the stability of the attractor network model of perceptual bistability in the steady state, and then enhances it; and (iii) the noise intensity P or departure q from the Gaussian noise only enhances the stability of the attractor network model of perceptual bistability in the steady state.     

确定峰度非高斯海洋环境噪声模型研究

针对非高斯海洋环境噪声仿真问题,利用对衰减正弦信号均匀采样方法,产生了具有特定谱特性同时具有特定峰度值的非高斯海洋环境噪声序列。在理论仿真条件下,通过对低峰度值和高峰度值的分别讨论发现,当峰度值高于3.0时总可以仿真得到较好的结果,而当峰度值低于3.0时,需通过降采样或降阶的方法解决不能仿真的问题。4种海上试验条件下的仿真结果表明,在安静环境、单一航船干扰环境、气枪声源干扰环境以及冲击性干扰环境下,都可以产生与目标谱特性、统计特性几乎相同的非高斯海洋环境噪声序列。     

Coherence resonance induced by non-Gaussian noise in a deterministic Hodgkin-Huxley neuron

In this paper, we report a novel effect of a particular kind of non-Gaussian noise (NGN), especially its deviation from Gaussian noise, on the spiking activity in a deterministic Hodgkin-Huxley (HH) neuron. It is found via numerical simulations that the coefficient of variation (CV), characterizing the spiking regularity, nonlinearly changes with varying deviation and passes through a minimum at an optimal deviation value, representing the presence of the coherence resonance (CR). This phenomenon shows that, when the NGN is optimal, the neuron can exhibit the most regular firing behavior. This result provides a constructive role of the NGN in the timing precision of information processing and signal transduction in neural systems.     

Effects of non-Gaussian noise near supercritical Hopf bifurcation

We have studied the effects of non-Gaussian colored noise in a chemical oscillation system, the well-known Brusselator model, in the parameter region close to the supercritical Hopf bifurcation. With the variation of the parameter q, which quantifies the deviation from Gaussian character, the signal-to-noise ratio of noise induced oscillation exhibits a bell-shaped change, indicating the presence of resonant activity. The cooperative effects of q and the correlation time τ on the performance of noise induced oscillation are also investigated. Interestingly, resonance-like behavior can be induced by either q or τ when the other parameter is properly fixed. Stochastic normal form theory is used to analyze these nontrivial effects and the simulation results are well reproduced. This work provides us comprehensive understanding of how non-Gaussian noise influences the dynamics in chemical oscillation systems.     

Influence of the colored noise on determining the period of a torsion pendulum

Based on statistical properties, two typical models are considered to calculate the uncertainties for some random noise sequences on the period extraction of a torsion pendulum, which is important and instructive in the measurement of gravitational constant G with the time-of-swing method. An expression of the uncertainty for the period measurement is obtained, which is dependent on the ratio ?t/(1/λ) where ?t is the interval of the sample time and 1/λ is the length of the correlation time. The result of processing experimental data shows that as the interval of the sample time ?t gradually shortens, the uncertainty of the period becomes smaller, and further when the ratio ?t/(1/λ) is less than 1, the uncertainty remains substantially unchanged.     

Multiplicative non-Gaussian noise and additive Gaussian white noise induced transition in a piecewise nonlinear model

We study the transition problems in a piecewise nonlinear model induced by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Firstly, applying the path integral approach, the unified colored noise approximation, the analytical expression of the steady-state probability density function (SPD) is derived. Then the change regulation of the SPD is analyzed with the change of the strength and relevance of multiplicative noise and additive noise. From numerical computations we obtain some new nonlinear phenomena: the transition can be induced by the cross-correlation strength between noises, the non-Gaussian noise intensity and the Gaussian noise intensity as well as the non-Gaussian noise deviation parameter. This indicates that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. Moreover, we also find the correlation time of the non-Gaussian noise can not induce the transition.     

基于传声器阵列过顶测量结果的飞机起落架噪声研究

应用由111个传声器组成的平面传声器阵列对当前流行的民用客机进场着陆过程中的机体噪声源进行了实验测量,本对七架窄体客机和七架宽体客机的起落架噪声进行了分析,得到了起落架噪声的频谱特性、指向特性和声级变化。研究发现,起落架噪声的频谱是由宽频随机噪声与一些较为明显的单噪声源组成,起落架噪声的指向性类似于一个水平放置的偶极子。不同飞机起落架噪声的声级相差较大,这说明可以通过重新结构设计降低起落架噪声。     

一种快速产生数字式高精度高斯噪声的新方法

伪随机噪声在信号分析和信号处理中具有重要的实用价值，高晰随机信号是一种最常用的信号形式，本文给出一种产生高斯噪声序列的新方法，利用先进的ＤＳＰ芯片编程技术，将高速产生的均匀分布噪声进行抽样变换，得到了高精度的高斯分析噪声序列，因此这种方法产生的高斯噪声统计特性好，周期长，性能稳定，符合声纳和通信等有关领域的要求，本文给出了原理分析，系统设计及实际应用结果。     

Effects of image processing on the noise properties of confocal images

The effects on the noise content of producing a projection from a stack of confocal images are investigated. Processing by retaining either the mean or peak pixel value is found to reduce noise, with the former giving more noise reduction. Gaussian noise, shot noise and speckle are considered. The effects of processing on the perception of the images are discussed.     

Linear relaxation times of stochastic processes driven by non-Gaussian noises

The linear relaxation time (LRT) associated with steady-state correlation functions is studied for Langevin equations with non-Gaussian noises: dichotomous Markov noise and Poissonian white shot noise. Exact results for arbitrary models are obtained and compared with results for Gaussian noises. Some general features of LRTs are discussed. The concept of dynamic effective diffusion is introduced and the existence of an optimal effective Fokker-Planck approximation is discussed. Explicit examples for prototype models are presented and briefly compared with the analogs for Gaussian noises.     

弱噪声极限下二维布朗运动的随机共振现象

在弱噪声极限下，应用多维Fokker-Planck方程的与时间有关问题方面的理论，推导了对称双稳势阱中二维布朗粒子的概率跃迁速率，并基于绝热近似理论研究了弱噪声极限下受小幅低频周期力驱动的二维布朗运动的随机共振现象.与以前的结果相比，所得到的信噪比与阻尼系数的大小无关.精确的数值模拟结果进一步说明了所得的信噪比的适用性. 关键词： 二维布朗运动 弱噪声极限 随机共振 信噪比