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´e criterion, we also show that the order 1 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 maximum 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.