具有无限时滞中立型泛函微分方程零解的渐近性态

本文利用 D算子的某些性质及 Liapunov泛函的方法 ,研究了具有无限时滞中立型泛函微分方程零解的一致稳定性与一致渐近稳定性 ,得到了新的结果 .     

具有无限时滞中立型泛函微分方程零解的渐近性态

本文利用D算子的某些性质及Liapunov泛函的方法,研究了具有无限时滞中立型泛函微分方程零解的一致稳定性与一致渐近稳定性,得到了新的结果。     

带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定性

研究了带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定性问题.通过构造合适的Lyapunov泛函,得到了判定带马尔可夫跳的时滞随机递归神经网络的以分布渐近稳定的充分条件.并举例说明结论的有效性.     

G-Brown运动驱动的中立型随机时滞微分方程的指数稳定性

研究了一类G-Brown运动驱动的中立型随机时滞微分方程的指数稳定性.在G-框架意义下,运用合适的Lyapunov-Krasovskii泛函,中立型时滞微分方程理论以及随机分析技巧,证明了所研究方程平凡解的p-阶矩指数稳定性,得到了所研究方程平凡解是p-阶矩指数稳定的充分条件.最后通过例子说明所得的结果.     

中立型带跳不确定变时滞随机系统鲁棒指数稳定

研究了一类中立型Markov跳变随机系统鲁棒指数稳定性,借助于Lyapunov-Krasovskii 泛函方法和随机稳定性理论,给出并证明了使中立型Markov跳变时滞随机系统指数稳定的充分条件,所有结果以线性矩阵不等式形式给出,算例表明了所给出的稳定性判据的有效性.     

一类多时滞中立型广义系统的稳定性判据

研究了多时滞的中立型广义时滞系统时滞相关的渐近稳定性问题,利用Lyapunov-Krasovskii泛函,等价模型转换方法和自由由权矩阵的方法,给出了系统时滞相关渐近稳定的充分条件,所给的判据是线性矩阵不等式形式,可方便运用Matlab工具箱求解,最后用一实例验证了方法的有效性。     

无限时滞随机泛函微分方程的Razumikhin型定理

在无限时滞的随机泛函微分方程整体解存在的前提下,建立了一般衰减稳定性的Razumikhin型定理.在此基础上,基于局部Lipschitz条件和多项式增长条件,得到了无限时滞随机泛函微分方程整体解的存在唯一性,以及具有一般衰减速率的p阶矩和几乎必然渐近稳定性定理.     

中立多变时滞Volterra型随机动力系统的稳定性

探讨了一类非线性随机积分微分动力系统,并通过Banach不动点方法,给出了该系统零解均方渐近稳定的充要条件,形成了中立多变时滞Volterra型随机积分微分动力系统零解均方渐近稳定性定理。与前人的研究方法不同,该文根据多变时滞随机动力系统各时滞的特点,灵活构造算子,相比以往文献的方法更加灵活实用。文章的结论一定程度上改进和发展了相关研究论文的结果。另外,文章所得结论补充并推广了不动点方法在研究非线性中立多变时滞Volterra型随机积分微分动力系统零解稳定性方面的成果。     

一类非线性无穷时滞中立型泛函微分方程系统的一致稳定性

本文讨论一类无穷时滞非线性中立型泛函微分方程解的渐近性态与零解的一致稳定性，得到若干简单的稳定性判据。     

超中立型泛函微分方程的稳定性及其应用

关于超中立型泛函微分方程零解的一致稳定、一致渐近稳定及强渐近稳定等有关理论,文献[4—6]在时滞r(t)满足:0<τ≤ r(t)≤r的条件下,利用V函数法进行了研究.本文中,在放弃时滞r(t)上述限制的情况下,通过建立一类重要的向量微分差分不等式,得到了超中立型泛函微分方程(包括无界时滞系统)零解在度量空间C中的全局指数稳定性及渐近稳定性的若干具体、简洁的充分判定准则,避免了求P函数的困难.作为应     

随机延迟微分方程的数值方法的收敛性和稳定性

本文研究了随机延迟微分方程的平衡方法的收敛性和均方稳定性.利用半鞅收敛定理,给出了真解的渐进稳定和均方稳定的一个更弱的条件.平衡方法下随机延迟微分方程的真解的均方稳定性.     

Asymptotic properties of neutral stochastic differential delay equations

This paper discusses asymptotic properties, especially asymptotic stability of neutral stochastic differential delay equations. New techniques are developed to cope with the neutral delay case, and the results of this paper are more general than the author's earlier work within the delay equations     

一类三阶中立型时滞微分方程的渐近稳定性

讨论了一类三阶中立型时滞微分方程的零解的渐近稳定性,借助于构造函数、推广的Halanay一维时滞微分不等式及泰塔格利亚公式,得到了判定其零解是渐近稳定的且与时滞无关的一个充分条件.     

不确定中立型线性随机时滞系统的鲁棒稳定性

建立了中立型随机微分时滞方程的LaSalle不变原理,然后应用LaSalle不变原理讨论了不确定中立型随机时滞系统的随机渐近稳定和几乎必然指数稳定的代数判据, 同时给出示例说明结果的有效性．     

General decay pathwise stability of neutral stochastic differential equations with unbounded delay

Without the linear growth condition, by the use of Lyapunov function, this paper establishes the existence-and-uniqueness theorem of global solutions to a class of neutral stochastic differential equations with unbounded delay, and examines the pathwise stability of this solution with general decay rate. As an application of our results, this paper also considers in detail a two-dimensional unbounded delay neutral stochastic differential equation with polynomial coefficients.     

Asymptotic Stability of Runge-Kutta Methods for the Pantograph Equations

This paper considers the asymptotic stability analysis of both exact and numerical solutions of the following neutral delay differential equation with pantograph delay.where $B,C,D\in C^{d\times d},q\in (0,1)$,and $B$ is regular. After transforming the above equation to non-automatic neutral equation with constant delay, we determine sufficient conditions for the asymptotic stability of the zero solution. Furthermore, we focus on the asymptotic stability behavior of Runge-Kutta method with variable stepsize. It is proved that a L-stable Runge-Kutta method can preserve the above-mentioned stability properties.     

Stability analysis of block boundary value methods for neutral pantograph equation

This paper deals with the convergence and stability properties of block boundary value methods (BBVMs) for the neutral pantograph equation. Due to its unbounded time lags and limited computer memory, a change in the independent variable is used to transform a pantograph equation into a non-autonomous differential equation with a constant delay but variable coefficients. It is shown under the classical Lipschitz condition that a BBVM is convergent of order p if the underlying boundary value method is consistent with order p. Furthermore, it is proved under a certain condition that BBVMs can preserve the asymptotic stability of exact solutions for the neutral pantograph equation. Meanwhile, some numerical experiments are given to confirm the main conclusions.     

Convergence of numerical solutions to neutral stochastic delay differential equations with Markovian switching

Recently, numerical solutions of stochastic differential equations have received a great deal of attention. It is surprising that there are not any numerical methods established for neutral stochastic delay differential equations yet. In the paper, the Euler–Maruyama method for neutral stochastic delay differential equations is developed. The key aim is to show that the numerical solutions will converge to the true solutions under the local Lipschitz condition.     

RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.     

无限时滞中立型随机泛函微分方程解的存在唯一性

有限时滞随机泛函微分方程的存在唯一性已经得到较多的研究,但对于无限时滞随机泛函微分方程的性质极少.本文在不需要线性增长条件,在一致Lipschitz条件下证明了无限时滞中立型随机泛函微分方程的存在唯一性,给出了精确解和近似解的误差估计,最后给出了解的矩估计.