Enhancement of density divergence in an insect outbreak model driven by colored noise

The steady states and the transient properties of an insect outbreak model driven by Gaussian colored noise are studied in this paper.According to the Fokker-Planck equation in the unified colored-noise approximation,we analyse the stationary probability distribution and the mean first-passage time of this model.By numerical analysis,the effects of the self-correlation time of insect birth rate and predation rate respectively reveal a manifest population divergence on the insect density.The decrease of the mean first-passage time indicates an enhancement dynamic on the density divergency with colored noise of a large self-correlation time based on the insect outbreak model.     

色关联噪声驱动下非线性神经元模型的相干共振

研究了关联的加性离子通道噪声和乘性突触噪声共同作用下非线性积分发放神经元模型中的相干共振现象.运用绝热近似理论和统一色噪声近似方法,得到了神经元首次点火概率分布和神经元放电峰峰间隔的变差系数的近似表达式.研究表明,首次点火概率分布和变差系数是突触噪声强度、离子通道噪声强度、乘性色噪声自相关时间和噪声关联强度的函数,适当的噪声强度、噪声自相关时间和噪声关联强度可以减小神经元发放峰峰间隔的变差系数,使系统的相干性达到最大值,从而引起神经元出现相干共振现象.同时讨论了离子通道噪声强度、突触噪声强度、乘性色噪声自相关时间和噪声关联强度对系统相干共振的影响.     

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.     

色噪声驱动的双奇异随机系统随时间演化的熵变化率上界

通过变换的方法讨论了一类高斯色噪声驱动的双奇异随机系统所对应的Fokker-Planck方程, 并结合Shannon信息熵的定义及Schwartz不等式原理给出了经变换后该系统随时间演化的熵变化率上界的精确表达式. 分析了奇异性强度参数、噪声相关时间与耗散参数对熵变化率上界的显著影响.     

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.     

平方泵噪声驱动的单模激光立方模型及光强定态概率分布

合理地引入了平方泵噪声到单模激光的立方模型中. 得到封闭的光强朗之万方程. 基于作者早期关于非线性外噪声的近似福克-普朗克方程(AFPE)的工作，得到了光强概率分布的AFPE，求出了该AFPE的归一化定态概率分布的精确解析表达式，并根据表达式对泵噪声实部和虚部之间的关联系数λ的对称性，得出了若干关于系统定态统计性质的普遍结论. 关键词： 平方泵噪声 单模激光的立方模型 光强定态概率分布 统计性质重复出现     

On the Lifschitz singularity and the tailing in the density of states for random lattice systems

We prove rigorously the existence of a Lifschitz singularity in the density of states at zero energy in some random lattice systems of noninteracting bosons and fermions in any numberv of dimensions. The basic tool is a simple modification of the method of Fukushima to yield the correct upper and lower bounds for allv. We also comment on the mathematical difference between the models treated and the system of phonons with mass disorder in the harmonic approximation, whose behavior is known to be of Debye form, not Lifschitz, at low temperatures.Supported by the Swiss National Science Foundation.On leave of absence from the Institute de Fisica, University of São Paulo, Brazil.     

Problems of the electronic structure of nonmetals in a wide energy region of fundamental absorption (review)

The article surveys the main unsolved problems of the electronic structure of nonmetals in a wide energy region of fundamental absorption. Udmurtia State University, 71, Krasnogeroiskaya Str., Izhevsk, 426034, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 3, pp. 299–315, May–June, 1999.