状态反馈脉冲控制的Leslie-Gower害虫管理数学模型  

A Leslie-Gower Pest Management Model with Impulsive State Feedback Control

作　　者：魏春金[1] 陈兰荪[2] 

机构地区：[1]集美大学理学院,福建厦门361021 [2]中国科学院系统科学研究院,北京100080

出　　处：《生物数学学报》2012年第4期621-628,共8页Journal of Biomathematics

基　　金：国家自然科学基金资助项目(11171284);福建省自然科学基金资助(2012J01012);集美大学科研基金资助(ZC2011003);福建省教育厅基金资助(JA12198)

摘　　要：研究了食饵具有庇护效应的状态反馈脉冲控制的Leslie-Gower害虫管理数学模型,当害虫的数量达到经济危害水平时,通过释放天敌和喷洒农药使得害虫的数量不超过经济危害水平.我们首先利用微分方程几何理论和后继函数的方法得到系统阶1周期解的存在性,并给出了阶1周期解轨道渐近稳定的条件,最后利用数值模拟验证了主要结论.In this paper, a Leslie-Gower pest management model incorporating a prey refllge with impulsive state feedback control is proposed. When the pest, reaches the critica.1 case, the control measures are taken by spraying pesticide and releasing natural enemies to control the pest under the economic threshold. The sufficient conditions for existence of order-1 periodic solution are obtained by differential equation geometry theory and the method of successor function. The order-1 periodic solution of the system is orbitally asymptotically stable under some conditions. Numerical results are carried out to illustrate the feasibility of our main results.

关 键 词：半连续动力系统 害虫综合治理 阶1周期解 后继函数 

分 类 号：O175.12[理学—数学]