一类非线性扰动系统的L∞稳定性

针对一类带有扰动的非线性系统,在它的标称系统的自由动态是一致渐近稳定和它的标称系统存在ISS-Lyapunov函数条件下,运用Lyapunov方法,得出该类系统是小信号L_∞稳定和L_∞稳定的充分条件.     

一类非定常经济系统的Lyapunov稳定性

讨论了一类非定常经济系统的Lyapunov稳定性,给出了经济系统稳定和渐进稳定的充分条件和稳定的必要条件,同时得到与系统稳定性有关的临界积累率的解析表达式.结果可为经济政策的制定提供理论依据.     

适应镇定了的AR系统的稳定性

由鞅差序列驱动的 ARX系统经适应镇定后导致闭环系统在均方意义稳定 ,但此时系统的稳定性并不清楚 .在噪声满足一定的条件下 ,本文证明了此闭环系统就是稳定的     

具有毒素和捕获作用的两种群竞争系统的稳定性分析

研究一类两种群无差别捕获的具有毒素作用的竞争系统.首先得到了系统存在唯一正平衡点的充分性条件;其次,通过构造适当的Lyapunov函数得到了保证该系统边界平衡点全局稳定的充分性条件;最后,在前人的基础之上得到了系统正平衡点全局渐近稳定的充分性条件,所得结果补充和完善了T.K.Kar和K.S.Chaudhuri的相应结果.     

矩阵系统的稳定与条件稳定

一个矩阵对应一种状态变换 .一系列的矩阵构成矩阵序列系统 .任一微小的扰动都会破坏伪逆的精确性 ,即状态的最后结果 .本文证明 :若矩阵系统是广义各态历经的 ,则系统是稳定的 ;若矩阵系统是普真的 ,则系统是条件稳定的 .     

血型分布的稳定性问题

在ABO血型系统中,各个民族、地区的血型分布情况极不同相同.但能长期稳定存在.本文通过建立血型遗传迭代数学模型对所给的数据进行处理,合理解释了各个民族血型分布能长期稳定原因.     

动态控制下Euler-Bernoulli梁的多项式镇定

考虑动态输出反馈控制下Euler-Bernoulli梁的振动抑制问题,证明了系统算子生成的C0-半群,不指数稳定但渐近稳定.且当初值充分光滑时,利用Riesz基方法估计出系统能量多项式衰减.     

带有时滞的非定常企业投资系统的Lyapunov稳定性

讨论了企业投资系统的Lyapunov稳定性,得到了企业投资系统渐进稳定的充分条件和稳定的必要条件,并给出了企业投资系统的临界积累率的表达式,这个问题的研究对于促进我国经济高速、稳定持续增长具有重要的理论意义和现实指导价值.     

具有时滞的生态流行病模型的稳定性和Hopf分支

该文考虑一类食饵染病的时滞捕食被捕食模型. 作者分析了系统的非负不变性, 边界平衡点的性质和全局稳定性. 证明了当时滞τ=τ\-1+τ\-2适当小时, 正平衡点是局部渐近稳定的,随着时滞的增加, 正平衡点由稳定变为不稳定, 系统在正平衡点附近发生Hopf分支.     

亚正定阵在Gilpin-Ayala系统稳定性中的应用

Gilpin-Ayala系统在正的平衡位置的稳定性历来是人们关注的重要问题,许多文献都对此进行过较为深入的研究,并且建立了判定该系统在正的平衡位置稳定的若干新方法.将亚正定阵引入到Gilpin-Ayala系统,获得了判定其稳定、渐近稳定的另一些新方法.     

Volterra系统全局稳定、扇形稳定及关联稳定的一些新判据

Stability of Volterra systems are discusses by subpositive definite matrix, and some new criterions for Volterra systems on overall situation stability, sector stability and connection stability are acquired. These results expand or improve some existing criterions.     

线性Volterra系统V泛函的构造及其应用

Ｖ泛函的构造是讨论Ｖｏｌｔｅｒｒａ积分微分系统稳定性的关键．近十年来，不少作者在Ｌｉａｐｕｎｏｖ泛函构造方面作了不少努力，但对一般的线性Ｖｏｌｔｅｒｒａ系统，还是没有构造Ｌｉｓｐｕｎｏｖ泛函通用而有效的方法．本文通过具体求解一个线性偏微分方程的方法来确定Ｖ泛函，得到了更广泛的Ｌｉａｐｕｎｏｖ泛函以及变号Ｖ泛函．同时，利用这些Ｖ泛函对线性Ｖｏｌｔｅｒｒａ系统的实用稳定性与Ｌｉｓｐｕｎｏｖ稳定性作了讨论．     

随机Volterra积分方程相容解的稳定性

本文考虑了随机Volterra积分方程相容解的稳定性.应用Lyapunov第二方法,并以推广的Ito公式为工具,给出了随机Volterra积分方程相容解的几乎确定指数稳定和矩指数稳定的充分性原则.     

Stability of discontinuous Cauchy problems in Banach space

We present Lyapunov stability results, including Converse Theorems, for a class of discontinuous dynamical systems (DDS) determined by differential equations in Banach space or Cauchy problems on abstract spaces. We demonstrate the applicability of our results in the analysis of several important classes of DDS, including systems determined by functional differential equations, Volterra integro-differential equations and partial differential equations.     

可修复系统适定性和稳定性

为了研究可修复系统适定性和稳定性,首先利用Co半群理论,研究了Volterra方程的适定性和渐进行为.其次利用特征线法求得系统方程的时间依赖解,通过边界条件将其转化为有限维空间上的Volterra方程.最后,由所建立的Volterra方程的相关结果,得到了可修复系统的适定性和稳定性.     

Positivity and uniform exponential stability for Volterra integro-dynamical systems on time scales

The main objective of this study is two-fold: First, we provide necessary and sufficient conditions for the positivity of Volterra integro-dynamical systems on time scales by means of Metzler matrices. Secondly, we show that positivity of the system implies uniform exponential stability of the trivial solution under sufficient conditions.     

Convergence and stability of extended block boundary value methods for Volterra delay integro-differential equations

In this paper, we construct a class of extended block boundary value methods (B₂VMs) for Volterra delay integro-differential equations and analyze the convergence and stability of the methods. It is proven under the classical Lipschitz condition that an extended B₂VM is convergent of order p if the underlying boundary value methods (BVM) has consistent order p. The analysis shows that a B₂VM extended by an A-stable BVM can preserve the delay-independent stability of the underlying linear systems. Moreover, under some suitable conditions, the extended B₂VMs can also keep the delay-dependent stability of the underlying linear systems. In the end, we test the computational effectiveness by applying the introduced methods to the Volterra delay dynamical model of two interacting species, where the theoretical precision of the methods is further verified.     

Asymptotic stability versus exponential stability in linear volterra difference equations of convolution type

It is shown that uniform asymptotic stability does not imply exponential stability in linear Volterra difference equations. However, if the kernel of the equation decays exponentially. then both concepts are equivalent as in the case of ordinary difference equations.     

Geometric approach for global asymptotic stability of three-dimensional Lotka–Volterra systems

In this paper, by applying the geometric criterion and time average property to Lotka–Volterra systems, some results for the global asymptotic stability of the systems are obtained. Furthermore, we consider Li–Wang Conjecture for a three-dimensional system which is transformed from a Lotka–Volterra system.     

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.