一类两种群随机生态系统的稳定性

利用构造广义二次三项式作为随机李雅普诺夫函数的方法讨论了两种群随机Volterra生态系统的全局渐近稳定性，并对一类特殊情形给出了全局渐近稳定性的充分判据，推广了常微系统已有结果．     

Lotka-Volterra型N-种群竞争系统的持久性和稳定性

本文研究一类具有无穷时滞的概周期Lotka-Volterra型N-种群竞争系统的持久性和全局渐近稳定性.一些新的充分条件被得到.     

具时滞广义Cohen-Grossberg神经网络的全局渐近稳定性

利用同胚映射原理、线性矩阵不等式和构造的Lyapunov泛函研究了一类Cohen-Grossberg神经网络平衡点的全局渐近稳定性,优化了现有文献中关于全局渐近稳定性的判据.     

一类多因素HIV模型的研究

研究了一类多因素HIV模型.建立了一个标准型的DI模型,证明了无病平衡点的局部渐近稳定性和全局渐近稳定性.     

一类三阶双滞量时滞微分方程的全局渐近稳定性

运用类比法构造Lyapunov函数,讨论了一类三阶双滞量时滞微分方程的全局渐近稳定性,给出了其零解全局渐近稳定的充分性准则.     

四阶非线性系统的全局渐近稳定性

运用构造李雅普诺夫函数的方法 ,研究了一类四阶非线性系统的全局渐近稳定性 ,给出了该系统零解全局渐近稳定的充分条件     

一类具有饱和发生率的SIVS吸毒模型的动力学分析

本文研究一类具有饱和传染率的SIVS传染病模型.首先利用Routh-Hurwitz判据和特征根方法,得到平衡点的局部渐近稳定性,其次证明系统的持久性和无病平衡点的全局渐近稳定性,并利用极限系统理论得到地方病平衡点的全局渐近稳定性.最后用数值模拟验证理论结果的正确性.     

一类新的变时滞中立型神经网络的全局渐近稳定性条件

研究了一类激活函数的状态变量带有微分时滞的中立型神经网络的稳定性问题.通过构造李亚普诺夫函数,并利用LMI分析技巧,获得了该类中立型神经网络的全局渐近稳定性的充分条件.最后通过实际算例验证了所得结果的有效性.     

带有标准发生率和信息干预的时滞SIRS传染病模型的稳定性分析

本文考虑一类具有标准发生率和信息干预的时滞SIRS传染病模型.通过分析模型的特征方程,讨论无病平衡点和地方病平衡点局部渐近稳定性.应用Halanay不等式对无病平衡点的全局渐近稳定性进行证明.通过构造适当的Lyapunov函数讨论地方病平衡点全局渐近稳定性.最后通过数值模拟分析一些重要参数对疾病传播的影响.     

一类具有Allee影响的捕食者-食饵扩散系统研究

讨论一类具有Allee影响的捕食者-食饵扩散模型解的整体性态.通过线性化方法和Lyapunov泛函方法分别证明了该模型正平衡点的局部渐近稳定性和全局渐近稳定性.     

关于泛函微分方程的完全渐近稳定性定理

本文用两个李雅普诺夫V函数对泛函微分方程建立了完全渐近稳定性的一类判别定理.     

Strict stability of impulsive functional differential equations

Strict stability is the kind of stability that can give us some information about the rate of decay of the solutions. There are some results about strict stability of differential equations. In the present paper, we shall extend the strict stability to impulsive functional differential equations. By using Lyapunov functions and Razumikhin technique, we shall get some criteria for the strict stability of impulsive functional differential equations, and we can see that impulses do contribute to the system's strict stability behavior.     

Eventual practical stability of impulsive differential equations with time delay in terms of two measurements

In this paper we introduce a new stability—eventual practical stability for impulsive differential equations with time delay. By using Lyapunov functions and comparison principle, we will get some criteria of eventual practical stability, eventual practical quasistability and strong eventual practical stability for impulsive differential equations with time delay in terms of two measurements.     

Asymptotic stability and asymptotic solutions of second-order differential equations

We improve, simplify, and extend on quasi-linear case some results on asymptotical stability of ordinary second-order differential equations with complex-valued coefficients obtained in our previous paper [G.R. Hovhannisyan, Asymptotic stability for second-order differential equations with complex coefficients, Electron. J. Differential Equations 2004 (85) (2004) 1–20]. To prove asymptotic stability of second-order differential equations, we establish stability estimates using integral representations of solutions via asymptotic solutions and error estimates. Several examples are discussed.     

Razumikhin-type Theorems on Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay

The main aim of this paper is to study the stability of the stochastic functional differential equations with infinite delay. We establish several Razumikhin-type theorems on the exponential stability for stochastic functional differential equations with infinite delay. By applying these results to stochastic differential equations with distributed delay, we obtain some sufficient conditions for both pth moment and almost surely exponentially stable. Finally, some examples are presented to illustrate our theory.     

Exponential stability of energy solutions to stochastic partial differential equations with variable delays and jumps

In this work, we investigate stochastic partial differential equations with variable delays and jumps. We derive by estimating the coefficients functions in the stochastic energy equality some sufficient conditions for exponential stability and almost sure exponential stability of energy solutions, and generalize the results obtained by Taniguchi [T. Taniguchi, The exponential stability for stochastic delay partial differential equations, J. Math. Anal. Appl. 331 (2007) 191-205] and Wan and Duan [L. Wan, J. Duan, Exponential stability of non-autonomous stochastic partial differential equations with finite memory, Statist. Probab. Lett. 78 (5) (2008) 490-498] to cover a class of more general stochastic partial differential equations with jumps. Finally, an illustrative example is established to demonstrate our established theory.     

LambertW函数对一阶复时滞动力系统的稳定性分析

Lambert W函数具有的一些性质以及现今成熟的数学软件Maple等使得它能很好地应用于时滞微分方程的稳定性判别中.通过应用Lambert W函数对一阶复系数时滞微分方程渐近稳定性的判别命题,分析了一类参数反馈控制复系数时滞微分方程的稳定性,得到了更加精细的结果.相比已往的方法,新方法更简单、计算更方便并能快速有效的给出判定结果.     

两类两种群动力学方程的稳定性分析

本文研究两种群动力学方程平衡点的稳定性.讨论两个捕食者-食饵-领地模型,模型用1微分方程描述,模型2用积分微分方程描述.得出平衡点稳定的条件.所得结果指出可实现总体的种群稳定而不管局部的绝灭.     

Global attracting set,exponential stability and stability in distribution of SPDEs with jumps

A novel approach to the global attracting sets of mild solutions for stochastic functional partial differential equations driven by Lévy noise is presented. Consequently, some new sufficient conditions ensuring the existence of the global attracting sets of mild solutions for the considered equations are established. As applications, some new criteria for the exponential stability in mean square of the considered equations is obtained. Subsequently, by employing a weak convergence approach, we try to establish some stability conditions in distribution of the segment processes of mild solutions to stochastic delay partial differential equations with jumps under some weak conditions. Some known results are improved. Lastly, some examples are investigated to illustrate the theory.     

Stability analysis of fuzzy linear differential equations

Differential equation is a very important field of study not only in theory but in applications, and stochastic differential equation is also a significant branch of research in theory and applications. Based on the concepts of fuzzy process and fuzzy differential equation, we present some concepts of stability for fuzzy differential equations. Furthermore we propose the sufficient and necessary conditions of stability for fuzzy linear differential equations.