一类随机BAM细胞神经网络的指数稳定性

研究了一类随机BAM细胞神经网络的指数稳定性,利用Lyapunov函数理论、It公式和线性矩阵不等式方法,建立了这种细胞神经网络均方指数稳定性判定的充分性条件.     

一类脉冲随机神经网络的矩指数稳定性分析

基于数学归纳法,本文研究了一类脉冲随机神经网络的均方指数稳定和P阶矩指数稳定性问题,建立了具有更低保守性的矩指数稳定的充分条件.     

细胞神经网络的指数稳定性

该文研究了具有可变时滞的随机细胞神经网络的指数 稳定性,应用Razumikhin定理与Lyapunov函数,建立了这种细胞神经网络均方指数稳定与几乎必然指数稳定的两类判据,一类是时滞无关而另一类是时滞相关.     

具有随机扰动和多重变时滞的神经网络稳定性分析

考虑了一个具有多重时变时滞的随机神经网络的全局渐近稳定性问题.通过构造Lyapunov-Krasovskii函数并运用广义Ito公式,得到了一个充分条件,条件保证了神经网络在随机扰动下的全局均方渐近稳定性.最后通过一个数值实例验证了结果的有效性.     

无界可变延迟随机神经网络的指数稳定性（英文）

本文用Lyapunov函数方法和半鞅收敛定理研究无界可变延迟随机神经网络的指数稳定性.给出判定零解的均方指数稳定性和几乎必然稳定性的充分条件.本文所用的方法和结果适用于无界延迟系统,涵盖了已有文献中有界延迟系统的结果.     

随机Hopfield时滞神经网络均方指数稳定性: LMI方法

该文通过系统变换技巧, 构造出新型的Lyapunov泛函. 利用此Lyapunov泛函, 基于线性矩阵不等式, 得到了随机Hopfield时滞神经网络与时滞相关及与时滞无关均方指数稳定性新的充分条件. 数值例子表明, 与已有结果相比, 该文的结果具有较少的保守性.     

随机Cohen-Grossberg-type BAM神经网络的均方指数稳定性

通过构造Lyapunov函数,利用随机微分的It(ο)公式,研究了一类含有时滞的随机Cohen-Grossberg-type BAM神经网络的均方指数稳定性,并给出判定的条件,最后举例子说明结果的正确性.     

具脉冲混合时滞马尔可夫跳中立型随机神经网络系统指数稳定性

研究了具脉冲和混合时滞马尔可夫跳随机神经网络的鲁棒指数稳定性.通过构造合适Lyapunov-Krasovsii泛函,利用随机Lyapunov稳定性理论,给出并证明了该系统均方指数稳定性的充分条件,所有结果以线性矩阵不等式的形式给,数值算例表明无论脉冲是否发生在马尔可夫跳时刻,给出的稳定性标准都是有效的.     

分段连续型随机微分方程指数Euler方法的稳定性

给出了线性分段连续型随机微分方程指数Euler方法的均方指数稳定性.经典的对稳定性理论分析,通常应用的是Lyapunov泛函理论,然而,应用该方程本身的特点和矩阵范数的定义给出了该方程精确解的均方稳定性.以往对于该方程应用隐式Euler方法得到对于任意步长数值解的均方稳定性,而应用显式Euler方法得到了相同的结果.最后,给出实例验证结论的有效性.     

基于LMI方法的多时滞随机神经网络的指数稳定性

研究了一类具有多个时滞的随机神经网络的均方指数稳定性问题,应用Lyapunov-Krasovskii泛函稳定理论和线性矩阵不等式(LMI)方法,建立了该系统解的指数稳定判别准则,最后通过数值举例阐述了结果的有效性.     

一种改进的随机次梯度方法的快速收敛性

1引言考虑如下优化问题: min f(x)=sum from i=1 to m f_i(x),s.t. x∈X (1)其中,f_i∶R~n→R是凸函数且f_i不可微,X是R~n上的非空闭凸子集．解(1)的主要方法     

Long term behaviors of stochastic single-species growth models in a polluted environment II

This is a continuation of our paper [M. Liu, K. Wang, X. Liu. Long term behaviors of stochastic single-species growth models in a polluted environment. Appl Math Model 2011;35:752–62]. This work still devotes to studying three stochastic single-species models in a polluted environment. For the first system, sufficient criteria for extinction, stochastic non-persistence in the mean, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence of the population are established. The threshold between stochastic weak persistence in the mean and extinction is obtained. For the second model, sufficient conditions for extinction, stochastic non-persistence in the mean, stochastic weak persistence, stochastic weak persistence in the mean, stochastic strong persistence in the mean and stochastic permanence are established. The threshold between stochastic weak persistence and extinction is derived. For the third system, the threshold between stochastic weak persistence and extinction is obtained.     

Sampling and reconstruction for shift-invariant stochastic processes

In this paper, combining stochastic processes with shift-invariant spaces, we introduce shift-invariant stochastic processes. It is a general case of the classical band-limited stochastic processes and a kind of non-band-limited stochastic processes. Two sampling theorems are obtained for the shift-invariant stochastic processes. The results for band-limited stochastic processes and shift-invariant spaces are generalized by our new results.     

Stochastic stability and bifurcation for the chronic state in Marchuk’s model with noise

A stochastic differential equation modelling a Marchuk’s model is investigated. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Firstly, the stochastic Marchuk’s model has been simplified by applying stochastic center manifold and stochastic average theory. Secondly, by using Lyapunov exponent and singular boundary theory, we analyze the local stochastic stability and global stochastic stability for stochastic Marchuk’s model, respectively. Thirdly, we explore the stochastic bifurcation of the stochastic Marchuk’s model according to invariant measure and stationary probability density. Some new criteria ensuring stochastic pitchfork bifurcation and P-bifurcation for stochastic Marchuk’s model are obtained, respectively.     

A maximum principle for Markov regime-switching forward–backward stochastic differential games and applications

In this paper, we present an optimal control problem for stochastic differential games under Markov regime-switching forward–backward stochastic differential equations with jumps. First, we prove a sufficient maximum principle for nonzero-sum stochastic differential games problems and obtain equilibrium point for such games. Second, we prove an equivalent maximum principle for nonzero-sum stochastic differential games. The zero-sum stochastic differential games equivalent maximum principle is then obtained as a corollary. We apply the obtained results to study a problem of robust utility maximization under a relative entropy penalty and to find optimal investment of an insurance firm under model uncertainty.     

Global random attractors for the stochastic dissipative Zakharov equations

The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors wiil be obtained by decomposition of solutions.     

Strong solutions for stochastic partial differential equations of gradient type

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a genuinely new method of weighted Galerkin approximations based on the “distance” defined by the quasi-convex function. Spatial regularization of the initial condition analogous to the deterministic case is obtained. The results yield a unified framework which is applied to stochastic generalized porous media equations, stochastic generalized reaction–diffusion equations and stochastic generalized degenerated p-Laplace equations. In particular, higher regularity for solutions of such SPDE is obtained.     

Stabilization of stochastic systems under Markovian switching

The problem of state feedback stabilization of discrete-time stochastic processes under Markovian switching is considered. The jump Markovian switching is modeled by a discrete-time Markov chain, and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Necessary and sufficient conditions based on linear matrix inequalities (LMI’s) for stochastic stability is obtained. The proposed control law for this stochastic stabilization result depends on the mode of the system as well as the environmental disturbances. The robustness results of such stability concepts against all admissible uncertainties are also investigated. An example is given to demonstrate the obtained results.     

Passivity analysis of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations

This paper is concerned with the passivity problem for a class of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations. Some sufficient conditions are obtained to guarantee that the complex dynamic networks with multiple time-varying delays and stochastic perturbations under Markovian switching are passive in the sense of expectation. The appropriate stochastic Lyapunov–Krasovskii functional was constructed, and stochastic theory, linear matrix inequality technique and properties of Weiner process were employed to achieve the results. Finally, some simulation examples are presented to illustrate the effectiveness of the obtained results.     

与年龄相关的随机分数阶种群系统温和解的存在性、唯一性

本文研究了一类与年龄相关的随机分数阶种群动态系统.利用不动点定理、随机分析和算子半群理论,讨论了与年龄相关的随机分数阶种群系统温和解的存在性、唯一性.本文是随机整数阶种群系统的推广.