Global asymptotic stability in n-species nonautonomous Lotka–Volterra competitive systems with infinite delays

By means of Lyapunov functional, we have succeeded in establishing the global asymptotic stability of the positive solutions of a delayed n-species nonautonomous Lotka–Volterra type competitive system without dominating instantaneous negative feedbacks. As a corollary, we show that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.     

广义的Lotka—Volterra方程的全局渐近稳定性

通过构造李亚普诺夫函数的方法,研究了广义的Lotka—Volterra时滞模型方程,而且给出了正平衡点的全局渐近稳定性的充分必要条件,同时对前人的结果进行了改进和推广．     

Stability for impulsive functional differential equations with infinite delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.     

具有变时滞的五种群Lotka-Volterra混合系统的正周期解

本文研究了具有变时滞的五种群Lotka-Volterra混合模型.通过使用泛函微分方程的单调流理论和Schauder不动点定理,获得了该系统的正周期解的存在性的充分条件,并建立了正周期解全局渐近稳定判别准则,改进和推广了已有的结果.     

On Stability of Solutions of a Certain Fourth—Order Functional Differential Equations

Using a Razumikhin-type theorem,we obtain sufficient conditions for the global asymptoticstability of the zero solution of a certain fourth order functional differential equations.The resultgeneralizes the well known results.     

Uniform asymptotic stability for damped linear oscillators with variable parameters

In this paper, sufficient conditions for uniform asymptotic stability of the damped linear oscillators with variable coefficients are presented. The result of the present study can be applied to even the case of negative damping. The conditions presented herein are shown to be essential for uniform asymptotic stability.     

STABILITY ANALYSIS OF HOPFIELD NEURAL NETWORKS WITH DELAYS

１ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙ，ｔｈｅａｒｔｉｆｉｃｉａｌｎｅｕｒａｌｎｅｔｗｏｒｋｓｈａｖｅｂｅｎｗｉｄｅｌｙａｐｐｌｉｅｄｉｎｓｏｌｖｉｎｇｐａｔｅｒｎｒｅｃｏｇｎｉｔｉｏｎ，ａｎｄｓｉｇｎａｌａｎｄｉｍａｇｅｐｒｏｃｅｓｉｎｇ，ａｎ...     

ASYMPTOTIC PROPERTY FOR A LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH DELAYS AND DISPERSION

An n-species nonautonomous Lotka-Volterra competition and diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and by using the skill of constructing an appropriate Lyapunov function, the new sufficient conditions are obtained for the global asymptotic stability and the uniqueness of the positive periodic solution.     

五种群Lotka-Volterra混合系统的全局渐近稳定性

考虑周期系数的五种群Lotka-Volterra模型,种群间既有捕食关系又有竞争关系,得到该系统的正周期解的存在性及全局渐近稳定性的条件.     

具无穷时滞的Lotka-Volterra捕食系统的生存分析

研究了具有无穷时滞具有m个捕食者和n个食饵的的Lotka-Volterra非自治系统,主要利用比较定理得到了系统内生物种群持续生存的充分条件.     

ON CRITERIA FOR GLOBAL STABILITY OF N-DIMENSIONAL LOTKA-VOLTERRA SYSTEMS

This paper gives the conditions for the existence of a globally stable equi-librium of rz-dimensional Lotka-Volterra systems in the following cases: Lotka-Volterra chain systems and Lotka-Volterra modei between one and multispecies. The conditions obtained in this paper are much weaker than those in [6] and more easily verifiable in application. So the results can be applied to more general Lotka-Volterra models. At the same time, the existence and stability conditions of positive equilibrium points of the above systems are given.     

一类三阶非线性时滞系统的全局渐近稳定性

运用"类比法"对一类三阶非线性时滞系统构造了较好的Lyapunov函数,得到该系统零解全局渐近稳定的充分条件.     

具有无穷时滞的中立型积分微分系统的平稳振荡

利用重合度理论中的延拓定理和微分积分不等式讨论具有无穷时滞的中立型积分微分系统其中x(t)=(x1(t),…,xn(t))T,G∈C2(Rn,R),f∈C(R×R×Rn×Rn,Rn),e∈C(R,Rn),e(t ω)≡e(t),f(t ω,u ω,x,y)≡f(t,u,x,y),f(t,u,0,0)≡0,t,u∈R,x,y∈Rn,ω>0为常数,获得了该系统平稳振荡的易于检验的判别条件.     

UNIFORMLY ASYMPTOTIC STABILITY FOR DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

11血roductlonAssume that BC(H)＝{p:(一 co,0]一R Is continuous and 11 yi 11二sup卜(。)l三 H}and that F:[0;＋比)X BC(H)一 Ris a given cofltiflllollSs＜0function;such that F(·,0)三 0．A＞0 Is a constant．Consider one－dimensionaldel叫dl俭rentlal equationX川＋入X(z)＝*I,X;)．(1〕In addition to the conditions above F also satisfies same conditions such thatthe SOllltiofl Of Eq．(1)x(t)＝x(t; to;i)llllqllely eXIStS Oil壬to;十①)for。11[to;i) E R＋ X BC(H(See [*])．FOr every yi …     

具有无穷时滞的Lotka-Volterra食物链模型的全局吸引性

研究一类具有无穷时滞的n种群Lotka Volterra食物链系统 .通过构造适当的Lya punov泛函 ,得到了保证该系统正平衡点全局吸引的充分条件 .     

具有阶段结构的竞争系统的持久性和稳定性

研究带有时滞和成长阶段的两种群竞争模型,第一个种群分成年和幼年两个阶段,第二个种群不具有阶段结构.本文证明了系统正解的有界性;利用比较原理得到了系统永久生存的充分条件;通过构造Lyapunov函数得到了系统全局渐近稳定的充分条件.     

一类具有阶段结构的三种群竞争系统

对一类具有阶段结构的三种群竞争系统进行了分析,得到了边界平衡点的全局渐近稳定性条件.