一类具季节性时变参数和脉冲控制的捕食-被捕食系统的动力学  

Dynamic Analysis of An Impulsively Controlled Predator-Prey Model with Seasonally Varying Parameters

作　　者：刘华祥[1] 曾广洪[2] 

机构地区：[1]广东海洋大学数学系,广东湛江524088 [2]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《南昌大学学报（理科版）》2010年第6期545-553,560,共10页Journal of Nanchang University(Natural Science)

基　　金：广东海洋大学科研资助项目(0612163)

摘　　要：研究一类脉冲控制的微分动力系统,该系统基于具有一般功能反应和季节性影响的捕食-被捕食系统,并加入了脉冲控制扰动,用来模拟农业生产中包括生物防治和化学防治在内的虫害综合防治过程或其他生物资源开发过程。利用脉冲微分方程中的Floquet理论和比较方法分析了该系统的动力学性质,建立了被捕食者绝灭周期解局部渐近稳定及全局渐近稳定的充分条件,后者对应着捕食-被捕食系统所反映的虫害综合防治策略的成功。最后运用多Lyapunov函数的比较方法证明了该系统在一定条件下是持久生存的。Based on the predator-prey system with general functional response and seasonal effects,an impulsive differential system to model the processes of integrated pest management involving biological control and chemical control in agriculture or the biological resources development is proposed and investigated.The dynamics of the system are analyzed using the Floquet theory and comparison techniques of impulsive differential equations.Sufficient conditions for the local asymptotic stability and the global asymptotic stability of the prey-eradication periodic solution are established,respectively,the latter corresponding to the success of the integrated pest management strategy from which our predator-prey system arises.Further,it is proven that this system is permanent under some conditions via a comparison method involving multiple Lyapunov functions.

关 键 词：脉冲控制 捕食-被捕食 稳定性 持久性 比较定理 FLOQUET理论 

分 类 号：O175.13[理学—数学]