具有脉冲扰动和非单调功能反应的三种群捕食系统的分析  

Analysis of a three-species predator-prey system with impulsive perturbations and non-monotonic functional response

作　　者：陈以平[1] 谢君辉[2] 

机构地区：[1]湖北民族学院理学院,湖北恩施445000 [2]湖南师范大学数学系,湖南长沙410081

出　　处：《纯粹数学与应用数学》2009年第2期332-338,共7页Pure and Applied Mathematics

基　　金：湖北省教育厅科研项目(B20082905);湖北省高等学校优秀中青年团队计划项目(T200804)

摘　　要：研究一类具有脉冲效应和非单调功能反应的两个捕食者一个食饵害虫控制系统.通过脉冲微分方程的Floquet理论和小幅扰动方法,证明了当脉冲周期小于某个临界值时,系统存在一个渐近稳定的害虫根除周期解,否则系统是持续生存的.最后,通过数值实例,给出了一简单讨论.A two-predator one-prey system with impulsive effect and non-monotone functional response for pest control is proposed and analyzed.By using the Floquet theory of impulsive differential equation and small amplitude perturbation skills, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Otherwise, the system can be permanent. Lastly, a brief discussion are given by numerical simulation.

关 键 词：两个捕食者一个食饵模型 脉冲作用 灭绝性 持续生存 

分 类 号：O175.12[理学—数学]