污染环境中一类捕食-食饵系统的持续性分析  

Analysis of Permanence for a Predator-Prey System in a Polluted Environment

作　　者：秦桂毅[1] 何德材[2] 黄文韬[2] 

机构地区：[1]桂林师范高等专科学校数学与计算机科学系,广西桂林541001 [2]桂林电子科技大学数学与计算科学学院,广西桂林541005

出　　处：《四川师范大学学报（自然科学版）》2011年第6期805-810,共6页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(10961011);广西自然科学基金(2010GXNSFC013012)资助项目

摘　　要：考虑一个周期性脉冲毒素输入的污染环境中的捕食者-食饵种群模型,研究了脉冲毒素输入对种群动力学行为的影响.利用脉冲微分方程的比较定理及函数积分均值的研究方法,得到了捕食者种群、食饵种群弱平均持续生存以及灭绝的阀值.利用maple软件实行了数值模拟,数值模拟显示了毒素的随机扰动对种群持续生存与灭绝的影响,在脉冲作用期较短时可能会导致种群的灭绝,而对于脉冲作用周期较长时,系统的持续生存不会受到严重影响.In this paper, we consider a predator-prey system with peliodic impulsive input of toxicant and study the effects of the toxicant on the species in a polluted environment. By using the impulse comparison theorem and the method of the integral mean value, we get the critical values for which the predator population as well as the prey population are weak mean permanence and extinct. Tile numerical simulation is taken by using mathematical software-Maple. It shows that stochastic perturbation of the toxicant affect in the permanence and extinction of the species. Stochastic perturbation may be result in the extinction of the species as the impulsive period is short, while for longer impulsive period, the permanent existence of the species isn＇ t badly affected by the stochastic perturbation of the toxicant.

关 键 词：脉冲微分方程 污染环境 持续生存 灭绝 

分 类 号：O175.12[理学—数学]