具有状态反馈脉冲控制的害虫管理SI模型的动力学性质  

The Dynamics of Pest Management SI Model with Impulsive State Feedback Control

作　　者：何志龙 聂麟飞[2] 

机构地区：[1]新疆财经大学金融学院,乌鲁木齐830012 [2]新疆大学数学与系统科学学院,乌鲁木齐830046

出　　处：《系统科学与数学》2017年第11期2163-2177,共15页Journal of Systems Science and Mathematical Sciences

基　　金：新疆维吾尔自治区自然科学基金(2016D01C046)资助课题

摘　　要：考虑到过量使用农药对环境和农作物造成的危害,文章提出了一类具有状态脉冲反馈控制策略的害虫管理SI控制模型,即,当易感害虫的数量到达经济危害水平时,施加生物和化学控制策略(例如,释放染病害虫且按易感害虫的比例喷洒杀虫剂),使得易感害虫的数量在极短的时间内低于危害阈值,从而达到控制病虫害的目的.通过使用微分几何理论,Poincaré映射,不动点定理等方法和技巧,建立了该控制模型系统正周期解存在性和稳定性的判别准则.Considering the harm caused by excessive use of pesticides on the en- vironment and crops, we propose a pest management SI model with state feedback impulsive control strategies, that is, when the quantity of susceptible pests popula- tion reaches the economic damage level, biological and chemical tactics （for example, the releasing infective pests, and spraying pesticides by rate of susceptible pest pop- ulation） are taken such that the quantity of susceptible pest population below the threshold value in a very short time, so as to achieve the purpose of insect pest con- trol. By using the method and skill of the geometry theory of differential equation,Poincar5 map and fixed point theorem, some criterions for the existence and stability of positive periodic solution are obtained.

关 键 词：害虫管理SI模型 状态反馈控制 POINCARE映射 周期解 存在性和稳定性. 

分 类 号：O175[理学—数学]