具有状态脉冲效应的阶段结构的害虫防治模型动力性分析(英文)  

Analysis of the Dynamics of Stage-structured Pest Control Model

作　　者：程惠东[1] 尹佐元[2] 刘洪霞[1] 

机构地区：[1]山东科技大学理学院,山东青岛266510 [2]山东科技大学信电学院,山东青岛266510

出　　处：《应用数学》2012年第4期816-823,共8页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (10872118)

摘　　要：本文对符合实际的具有状态脉冲效应的阶段结构的害虫防治模型进行研究,给出半连续动力系统、半连续动力系统的后继函数等的定义,根据动力系统的基本理论,采用脉冲微分方程几何理论的方法研究模型定义的半连续动力系统各种几何性质,得到系统存在阶1周期解的充分条件,阶1周期解全局轨道渐近稳定性的充分条件.获得的理论结果说明我们可以经过一次脉冲、两次脉冲、多次脉冲就能完全控制害虫使之不超过阖值.最后,我们用数值模拟的方法说明结果的正确性.In this paper,a stage-structured pest control model with state-dependent impulsive con- trol is considered. Firstly, the definitions of the semi-continuous dynamic systems, successor func- tions and order one periodic solution are introduced. Secondly, according to the differential equation geometry theory and the method of successor functions,the sufficient conditions for the existence, u- niqueness and orbitally asymptotical stability of order one periodic solution are obtained. The results show that,the pest population can be controlled below an economic injury level by applying effects impulsively once,twice,or at most,finite times. Finally,our results are confirmed by means of nu- merical simulation. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order one periodic solution.

关 键 词：半连续动力系统 阶一周期解 后继函数 轨道渐近稳定 

分 类 号：O175[理学—数学]