一类具有状态脉冲反馈控制的害虫治理模型  

A pest management model with state pulse feedback control

作　　者：黄立壮 刘琼 陈武大仁[2] 马艺铭 HUANG Li-zhuang;LIU Qiong;CHEN WU Da-ren;MA Yi-ming(College of Science,Beibu Gulf University,Qinzhou 535011, China;College of Mathematics and Information Science, Guangxi University, Nanning 530004, China)

机构地区：[1]北部湾大学理学院,广西钦州535011 [2]广西大学数学与信息科学学院,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2020年第4期911-919,共9页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自科基金青年基金资助项目(11701503);国家自科基金资助项目(71761001);广西自然科学基金资助项目(2016GXNSFAA380102)。

摘　　要：研究一类具有状态脉冲反馈控制的害虫治理模型。采用脉冲理论和微分方程的定性理论得到系统唯一的正平衡点是全局渐近稳定的;利用半连续动力系统几何理论获得系统阶1周期存在的充分条件,且存在的阶1周期解轨道是渐近稳定的。结果表明:在害虫治理过程中,根据害虫数量多少,实施人工脉冲干预的目的是要把害虫数量控制在允许的经济阈值之内,而不是彻底消灭害虫,这样可以保证对生态环境实现可持续发展。This article proposes a pest control model with state pulse feedback control.By using impulsive theory and qualitative theory of differential equations,it is found that the unique positive equilibrium point of the system is globally asymptotically stable;by using the geometric theory of semi continuous dynamical systems,the sufficient conditions for the existence of order 1 periodic solutions are obtained,and the existence of order 1 periodic solution orbits is asymptotically stable.The results show that the implementation of artificial pulse intervention based on the number of pests in the process of pest management is to control pests within the allowable economic threshold,instead of to eliminate pests completely,which can ensure the sustainable development of ecological environment.

关 键 词：状态脉冲 反馈控制 害虫治理 全局渐近稳定 正平衡点 

分 类 号：O175[理学—数学]