具有脉冲和时滞的Logistic模型的持续生存和正周期解的全局吸引性(英文)

GLOBAL ATTRACTIVITY OF THE POSITIVE PERIODIC SOLUTION OF A DELAY LOGISTIC POPULATION MODEL WITH IMPULSES

本文研究了具有脉冲和时滞效应的Logistic模型.利用脉冲微分方程的比较定理,Bohl-Brower不动点定理和Lyapunov函数法,获得了系统持续生存,正周期解存在、唯一以及全局吸引的充分条件.结果表明正周期解的全局吸引性与时滞有关.

In this article, a delay Logistic system governed by impulsive effects is investigated. By using comparison theorem, it is proved that the system is permanent under some appropriate conditions. Further, a set of sufficient conditions which guarantee the existence, uniqueness and global attractivity of positive periodic solution are obtained by using Bohl-Brower fixed point theorem and Lyapunov function. The result demonstrates that the global attractivity of the positive periodic solution depends on time delay.