害虫治理与半连续动力系统几何理论

文章编号: 1009-4822( 2011) 01-0001-09

陈兰荪^1，2

( 1． 中国科学院数学与系统科学研究院，北京    100080; 2． 福建师范大学闽南科技学院，福建 泉州    362332)

 

摘要: 从害虫治理的实际问题出发，建立了一类脉冲状态反馈控制害虫的防治模型． 提出了半连续动力系统几何理论，并应用这一理论证明了该模型至少存在一个阶 1 周期解． 结合具体实例，介绍了阶 1 同宿分支和脉冲环面动力系统的基本理论与分析方法．

 

关键词: 半连续动力系统; 脉冲微分方程; 害虫治理; 阶 1 周期解

中图分类号: O175． 14 文献标志码: A

 

作者简介: 陈兰荪( 1938 － ) ，男，教授，博士生导师，主要从事生物数学研究．

 

CHEN Lan-sun1，2

( 1． Academy of Mathematics and Systems Science，Chinese Academy of Science，Beijing 100080，China;

2． Minnan Science and Technology Institute，Fujian Normal University，Quanzhou 362332，China)

Abstract: Starting from practical problem of the pest control，a class of pest prevention model with impulsive feedback control is established． The geometric theory of semi-continuous dynamical systems is presented，and by applying this theory，it is proved for this model to have at least one order-one periodic solution． With the specific instance，the basic theory and analyzing method of the order-one homoclinic bifurcation and pulse torus power system are introduced．

Key words:  semi-continuous dynamical systems; impulsive differential equations; pest control; order-one periodic solution