具有脉冲效应和综合害虫控制的捕食系统  

PREDATOR-PREY SYSTEM WITH IMPULSIVE EFFECT AND INTEGRATED PEST CONTROL

作　　者：张树文[1] 陈兰荪[2] 

机构地区：[1]鞍山师范学院生物数学研究所,鞍山114005 [2]中国科学院数学与系统科学研究院数学研究所,北京100080

出　　处：《系统科学与数学》2005年第3期264-275,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(10171106;40372111)资助课题

摘　　要：本文通过生物控制和化学控制提出了具有周期脉冲效应与害虫控制的捕食系统. 系统保护天敌避免灭绝,在一些条件下可以使害虫灭绝.就是说当脉冲周期小于某一临界值时,存在全局稳定害虫灭绝周期解.脉冲周期增大大于临界值时,平凡害虫灭绝周期解失去稳定性并产生正周期解,利用分支理论来研究正周期解的存在性.进而,利用李雅普诺夫函数和比较定理确定了持续生存的条件.In this paper, predator-prey systems with periodic impulsive effect concerning pest control are proposed through biological control and chemical control. The model has the potential to protect natural enemies from extinction, but under some conditions may also serve to demonstrate the extinction of the pest, that is, there exists a global stable pest-eradication periodic solution when the impulsive period is less than some critical values. When the impulsive period increase, the trivial periodic pest-eradication solution loses its stability and a positive periodic solution comes out. The existence of a positive periodic solution is also studied by the bifurcation theory. Conditions for permanence is established via the method of comparison involving multiple Liapuno functions.

关 键 词：捕食系统 害虫控制 脉冲效应 李雅普诺夫函数 脉冲周期 解的存在性 保护天敌 化学控制 生物控制 全局稳定 正周期解 分支理论 持续生存 比较定理 临界值 灭绝 稳定性 

分 类 号：S433[农业科学—农业昆虫与害虫防治]