Global asymptotic stability and oscillation of a family of difference equations

We consider the family of difference equations of the form

     

具有可变时滞的非线性非自治差分方程的线性化全局渐近稳定性及其应用

证明了在一定条件下,具有可变时滞的非线性非自治差分方程的全局渐近稳定性可由某种线性差分方程的渐近稳定性确定,给出了这类差分方程全局渐近稳定的充分条件.作为实例,获得了具有可变时滞的离散型非自治广义Log istic方程的全局吸收性判别准则.     

Global stability results for impulsive differential equations

Global results concerning stability properties of impulsive differential equations are established, employing piecewise continuous Lyapunov functions which are then applied for proving stability and boundedness properties     

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．     

On the stability of nonautonomous difference equations

In this paper, we obtain new sufficient conditions for the asymptotic stability and instability of equilibrium points of the nonautonomous higher order difference equations by means of weak contractions and weak expansions.     

Global asymptotic stability of a family of difference equations

We consider the family of difference equations of the form

     

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.     

GLOBAL ASYMPTOTIC STABILITY OF THE PERIODIC LOTKA-VOLTERRA SYSTEM WITH TWO-PREDATORS AND ONE-PREY

The three species Lotka-Volterra periodic model with two predators and one prey is considered. A set of easily verifiable sufficient conditions is obtained. Finally, an example is given to illustrate the feasibility of these conditious.     

On the asymptotic stability in functional differential equations

Consider a system of functional differential equations where is the vector-valued functional. The classical asymptotic stability result for such a system calls for a positive definite functional and negative definite functional . In applications one can construct a positive definite functional , whose derivative is not negative definite but is less than or equal to zero. Exactly for such cases J. Hale created the effective asymptotic stability criterion if the functional in functional differential equations is autonomous ( does not depend on ), and N. N. Krasovskii created such criterion for the case where the functional is periodic in . For the general case of the non-autonomous functional V. M. Matrosov proved that this criterion is not right even for ordinary differential equations. The goal of this paper is to prove this criterion for the case when is almost periodic in . This case is a particular case of the class of non-autonomous functionals.

     

基于忆阻的时滞神经网络的全局稳定性

忆阻是近年来新发现的一类非线性电子元件．与通常的电阻不同,忆阻的阻值会随着通过的电流量的大小和方向不同而改变．这个特性使得忆阻具有了记忆的功能,在很多方面有着广泛的应用．该文给出了简化的忆阻的数学模型,基于该模型构造了时滞神经网络,利用微分包含理论、Lyapunov方法和同胚映射原理研究了其全局渐近稳定性问题,确保模型平衡点存在性、唯一性和一致全局渐近稳定性的充分条件被获得．最后提供的具有仿真的例子验证了获得的理论结果．     

On employment of semidefinite functions in stability of delayed equations

Four new stability theorems for nonautonomous delayed equations are established by the Lyapunov-Razumikhin approach with functions and its derivatives semidefinite. To do this, assume the collection of right-hand side translations in time has limit points which govern limiting equations. A corollary, which relates global asymptotic stability for the equation to that for limiting equations, and an illustrative example are given to show the applications of the established theorems.