带有Beddington-DeAngelis功能反应、脉冲、连续时滞和广义扩散函数的捕食者-食饵系统的定性分析  

Qualitative Analysis of Predator-prey System with Beddington-DeAngelis Functional Response,Impulsive,Continuous Delay and General Diffusion

作　　者：王烈[1] 陈斯养[1] 石茂[1] 

机构地区：[1]陕西师范大学数学与信息科学学院,西安710062

出　　处：《工程数学学报》2011年第3期323-334,共12页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(6067106310871122)~~

摘　　要：本文定性分析了具有Beddington-DeAngelis功能反应、脉冲、连续时滞和广义扩散函数的捕食者-食饵系统.利用脉冲微分方程的比较原理给出了系统持续生存的条件,并使用不动点理论证明了正周期解的存在性,进而给出了系统存在正周期解的充分条件.最后通过构造Lyapunov泛函证明了系统周期解的全局渐近稳定性.该结论可为现实的生物资源管理提供可靠的策略依据.A nonautonomous predator-prey model consisting of n-competing preys and one predator with the Beddington-DeAngelis functional response,impulsive,continuous delay and general diffusion is proposed.First,it is proved that the system is uniform persistence by using the comparing theorem of the impulsive system.Secondly,the existence of periodic solutions is proved through the Brower fixed point theory.Through constructing a Lyapunov mapping,the suffcient conditions for the existence of the positive periodic solution and the global asymptotic stability of the positive periodic solution are obtained.Our results provide a reliable tactic basis for the practical biological resource management.

关 键 词：捕食者-食饵系统 脉冲 时滞 正周期解 全局渐近稳定 

分 类 号：O175.7[理学—数学]