一类综合脉冲控制系统的动力学分析  

Dynamic Analysis of an Impulsive Model with Integrated Control

作　　者：唐甜[1] 李晓冬[1] 甘永莹 祝光湖[2] TANG Tian;LI Xiaodong;GAN Yongying;ZHU Guanghu(National Demonstration Center for Experimental Electronic Circuit Education,Guilin University of Electronic Technology,Guilin 541004,China;School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学电子电路国家级实验教学示范中心,广西桂林541004 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《信阳师范学院学报（自然科学版）》2020年第1期21-24,共4页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11661026);广西自然科学基金项目(2017GXNSFAA198235)

摘　　要：针对Lotka-Volterra的捕食-食饵系统提出了一个新的综合控制系统,利用三次脉冲微分方程拟合在一周期内不同时刻释放病虫和捕食者、喷洒农药以及投放病毒的动力学过程,从而达到控制害虫(食饵)的目的.根据Floquet定理和小振幅扰动方法,证明了当脉冲参数大于某个临界值时,系统存在一个全局渐近稳定的害虫灭绝周期解,并进一步获得了系统持续生存的条件.A new impulsive system with integrated control effects is presented based on Lotka-Volterra predatorprey systems.Impulsive differential equations with three impulsive effects in one period are used to simulate the behaviors of releasing sick pests and predators,spraying pesticides,and putting viruses for pest control.By using Floquet theorem and small amplitude perturbation methods,it is proved that there exists a globally stable pest eradication solution when the control parameters are larger than some critical values.The condition for the uniform permanence of this system is also presented.

关 键 词：捕食者-食饵系统 害虫综合治理 脉冲微分方程 稳定性 持续生存 

分 类 号：O175.13[理学—数学]