与年龄相关的随机时滞种群方程的指数稳定性

本文研究了与年龄相关的随机时滞种群方程,运用Burkholder-Davis-Gundy定理和改进的coercivity条件,建立了均方意义和几乎处处意义下与年龄相关的随机时滞种群方程稳定性的判定准则,得到了保证强解稳定的若干充分条件.     

变时滞混合随机微分方程的几乎必然指数稳定化（英文）

本文研究一类多维变时滞混合随机微分方程的几乎必然指数稳定性,方程具体形式:dy(t)=f(y(t-δ_1(t)),r(t),t)dt+g(y(t-δ_2(t)),r(t),t)dω(t),其中,δ_1(·),δ_2(·):R~+→[0,τ]表示变时滞,r(t)为一个Markov链.运用Lyapunov技巧,随机分析方法和BorelCantelli引理,该文证明了在一定的条件下,若此方程对应的混合随机微分方程:dx(t)=f(x(t),r(t),t)dt+g(x(t),r(t),t)dω(t)是几乎必然指数稳定的,则存在一个正常数τ,只要ττ,该方程也是几乎必然指数稳定的.这推广并改进了己有文献的一些结果.     

带跳随机微分方程的Euler-Maruyama方法的几乎处处指数稳定性和矩稳定性

本文首先研究了一维带跳随机微分方程的指数稳定性,并证明Euler-Maruyama(EM)方法保持了解析解的稳定性.其次,研究了多维带跳随机微分方程的稳定性,证明若系数满足全局Lipchitz条件,则EM方法能够很好地保持解析解的几乎处处指数稳定性、均方指数稳定性.最后,给出算例来支持所得结论的正确性.     

Khasminskii型条件下随机延迟微分方程$\theta$-方法的几乎必然指数稳定性[英文]

本文是我们之前工作的延伸, 本文作者和殷荣城(2013)在单调型条件下考察了随机微分方程的$\theta$ 方法的均方稳定性.在之前的结论中,我们考虑的是不带延迟的随机系统的均方稳定性.而本文, 我们希望进一步考虑带延迟的随机系统的几乎必然稳定性.本文在修改后的Khasminskii条件下得到随机延迟微分方程$\theta$方法的几乎必然指数稳定性. 该结果使现有结论得到可观的推进.     

Markov调制奇异随机微分方程的指数稳定性

建立了Markov调制奇异随机微分方程的p阶指数稳定性和几乎必然指数稳定性的充要条件．     

中立型随机比例微分方程的数值解的指数稳定性（英文）

本文主要利用半鞅收敛定理,研究中立型随机比例微分方程的数值稳定性.该文建立了线性的和非线性的中立型随机比例微分方程新的细则,我们将证明,在线性增长条件下,欧拉方法可以保留中立型随机比例微分方程的几乎处处指数稳定性,并且反向的欧拉方法能保留非线性的中立型随机比例微分方程的几乎处处指数稳定性.     

随机脉冲微分系统指数稳定性

该文首先给出了具有随机脉冲时刻影响的非线性微分系统 模型，然后得到了该模型零解的p阶矩指数稳定和几乎必然指数稳定的充分条件，在所得结果中不要求dV(t,x(t)) /dt定负．最后，给出一个例子说明所得结果的应用．     

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...     

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.     

随机时滞2D-Navier-Stokes方程的指数稳定性

由于流体受到某些遗传和不确定信息外力的影响,考虑了含时变时滞随机外力的2D-Navier-Stokes方程.借助随机分析中的It6公式和Burkholder-Davis-Gundy不等式,证明了大粘性系数情形方程整体弱解的均方指数稳定和几乎必然指数稳定.     

中立型随机泛函微分方程的均方指数稳定性

本文使用一类新方法研究中立型随机泛函微分方程的均方指数稳定性.由此,一些新的关于所考虑的方程解的均方指数稳定性结果被获得,一些已有的结果被改进.最后通过分析一些实例阐述了我们获得的理论的有效性.     

The Exponential Behaviour and Stabilizability of Stochastic 2D-Navier-Stokes Equations

Some results on the pathwise exponential stability of the weak solutions to a stochastic 2D-Navier-Stokes equation are established. The first ones are proved as a consequence of the exponential mean square stability of the solutions. However, some of them are improved by avoiding the previous mean square stability in some more particular and restrictive situations. Also, some results and comments concerning the stabilizability and stabilization of these equations are stated.     

Pseudo Almost Automorphic Solutions for Non-autonomous Stochastic Differential Equations with Exponential Dichotomy

In this paper, we consider the existence and uniqueness of the solutions which are pseudo almost automorphic in distribution for a class of non-autonomous stochastic differential equations in a Hilbert space. In conclusion, we use the Banach contraction mapping principle and exponential dichotomy property to obtain our main results.     

随机Volterra-Levin方程的稳定性

In this paper, we investigate the exponential stability in pth moment as well as the almost surely exponential stability of solutions of stochastic Volterra-Levin equations (SVLEs in short) by the use of fixed point theorem for p ≥ 2. Our results extend and improve the corresponding results obtained in [3, 12], and the result in [12] is a special case of our results.     

Stability Analysis for the Numerical Simulation of Hybrid Stochastic Differential Equations

This paper is mainly concerned with the exponential stability of a class of hybrid stochastic differential equations–stochastic differential equations with Markovian switching (SDEwMSs). It first devotes to reveal that under the global Lipschitz condition, a SDEwMS is pth (p ∈ (0,1)) moment exponentially stable if and only if its corresponding improved Euler-Maruyama(IEM) method is pth moment exponentially stable for a suitable step size. It then shows that the SDEwMS is pth(p ∈ (0,1)) moment exponentially stable or its corresponding IEM method with small enough step sizes implies the equation is almost surely exponentially stable or the corresponding IEM method, respectively. In that sense, one can infer that the SDEwMS is almost surely exponentially stable and the IEM method, no matter whether the SDEwMS is pth moment exponentially stable or the IEM method. An example is demonstrated to illustrate the obtained results.     

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. In this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.     

与年龄相关的随机时滞种群方程的指数稳定性

本文研究了与年龄相关的随机时滞种群方程,运用Burkholder-Davis-Gundy定理和改进的 coercivity条件,建立了均方意义和几乎处处意义下与年龄相关的随机时滞种群方程稳定性的判定准则,得到了保证强解稳定的若干充分条件．     

关于带跳中立型随机泛函微分方程p阶矩指数稳定性准则

本文研究了带跳中立型随机泛函微分方程的p阶矩指数稳定性,通过构造Lyapunov函数,运用分析的技巧得到了p阶指数稳定的准则.同时给出了一个例子显示出我们的结果是有效的.