具有脉冲效应的害虫传染病防治模型的动力学行为  

Dynamic Analysis of Pest-epidemic Model with Impulsive Control

作　　者：胡杰 刘娟[2] 赵清[3] HU Jie;LIU Juan;ZHAO Qing(School of Software,Shanxi Agricultural University,Taigu 030801,China;College of Arts and Sciences,Shanxi Agricultural University,Taigu 030801,China;College of Agriculture, Shanxi Agricultural University,Taigu 030801,China)

机构地区：[1]山西农业大学软件学院,山西太谷030801 [2]山西农业大学文理学院,山西太谷030801 [3]山西农业大学农学院,山西太谷030801

出　　处：《数学的实践与认识》2019年第2期304-310,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(31501876);山西省教育厅高等学校科技创新项目(2014131);山西省科技厅面上青年基金项目(201601D021122);山西农业大学科技创新基金项目(2017005;2017019)

摘　　要：基于害虫综合治理策略,建立了具有Monod-Haldance功能性反应的不同固定时刻分别投放染病害虫、天敌和喷洒化学农药的传染病模型.通过脉冲微分方程的小振动技巧、Floquet定理和比较定理,得到传染病模型中易感害虫灭绝周期解渐近稳定(局部和全局)的条件.并且利用Matlab软件通过调节相应的参数进行验证,得到模型的正确性.同时接下来可以继续深入研究的方向和课题.此模型的适用性很强,在农林业中可以用来指导实践.In the paper,we establish the pest-epidemic model with the Monod-Haldance functional response topresent the process of periodic spraying pesticide and releasing natural enemies and infected insect at different fixed moments.The sufficient conditions for the local stability and the globally stability of prey eradication periodic solution are obtained by using the Comparison theorem and Floquet theorem.Finally,we use numerical simulations to verify the feasibility of the obtained results by Matlab.At the same time,the problems that can be further studied in this paper are given.This model has strong applicability,which can be used to guide practices.

关 键 词：传染病防治模型 FLOQUET定理 Monod-Haldance功能性反应 渐近稳定性 MATLAB软件 

分 类 号：O175[理学—数学]