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.
出处
《工程数学学报》
CSCD
北大核心
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)~~
关键词
捕食者-食饵系统
脉冲
时滞
正周期解
全局渐近稳定
predator-prey system
impulsive
time delay
positive periodic solution
global asymptotic stability
