一类时滞差分方程的渐近稳定性

关于种群模型中常见的一类线性时滞差分方程的问题，国内外许多学者进行了一些有效的研究．但大部分讨论的都是确定方程中变系数为正、或常系数的差分方程问题．本文根据种群模型的实际背景，讨论了任意变系数方程利用直接方法获得了所讨论方程的零解的一致稳定和全局渐近稳定的充分条件，并举例说明了这两个充分条件不能相互代替。

The Asymptotic Stability of a Kind of Delay Difference Equations

Aiming at a kind of linear delay difference equations for species model,many mathematicians at home and abroad have made effective researches.Majority of the problems researched by them were confined to the difference equations with positive variable or constant coefficient.According to the model's actual background,discussing the random variable coefficient equation and using direct method,we obtain sufficient condition for the uniform stability and the globally asymptotic stability of difference equation,and also give examples to show they can not substitute each other.