一类状态依赖脉冲控制的害虫管理数学模型研究  

ON STUDY OF AN INTEGRATED PEST CONTROL MODEL WITH STATE DEPENDENT IMPULSIVE EFFECT

作　　者：师向云[1,2] 宋新宇[1] 

机构地区：[1]信阳师范学院数学与信息科学学院,信阳464000 [2]北京林业大学林学院,北京100083

出　　处：《系统科学与数学》2012年第7期799-810,共12页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11171284);河南省高校科技创新团队支持计划(2010IRTSTHN006);河南省科技创新杰出人才支持计划(104200510011);信阳师范学院青年骨干教师资助计划

摘　　要：研究一类状态依赖脉冲控制的害虫管理数学模型,当害虫的数量达到一定的临界值时,通过释放天敌和喷洒农药使得害虫的数量不超过经济危害水平.首先利用几何分析和后继函数方法得到了系统阶1周期解的存在性,进而运用类Poincare准则证明系统阶1周期解是轨道渐近稳定的.结论表明在一定的条件下,总能将害虫控制在经济危害水平以内,从而人们在农业生产过程中能够获得最大收益.证明系统存在阶1周期解的方法可推广到其它状态依赖脉冲反馈模型中.In this paper, we investigate the dynamic behavior of integrated pest control impulsive model by releasing natural enemies and spraying pesticide at some thresholds. By using geometric analysis and the successor function, we find the sufficient condition for existence of the order 1 periodic solution of the system. By using the analogue of the Poincar~ criterion, we also show that the order I periodic solution of the system is orbitally asymptotically stable under some condition. The results show that we can control the pest populations to the economic injury level under certain conditions, thus people can obtain the maxhnum return in agricultural production. The method used to prove the existence of the order 1 periodic solution of the system can be extended to other state-dependent impulsive models.

关 键 词：状态依赖脉冲微分方程 害虫综合治理 后继函数. 

分 类 号：O242.1[理学—计算数学]