捕食者具有阶段结构Holling Ⅱ类功能性反应的捕食模型正周期解的存在性以及全局吸引性  

Positive Periodic Solutions of a Delayed Predator-Prey System with Holling Type II Functional Response and Stage Structure for Predator

作　　者：陈凤德[1] 陈晓星[1] 张惠英[1] 

机构地区：[1]福州大学数学与计算机科学学院,福州350002

出　　处：《数学物理学报（A辑）》2006年第1期93-103,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(天元基金)(10426010);福建省青年科技人才创新基金(2004J002);福建省教育厅基金(JA04156);福州大学校科技发展基金(2003-XQ-21)资助

摘　　要：利用重合度理论中的延拓定理讨论了捕食者具有阶段结构Holling Ⅱ类功能性反应的捕食模型的正周期解的存在性,得到了保证周期解存在的充分性条件,推广了已知的相关结果．同时通过构造Lyapunov函数得到了保证周期解稳定性的充分性条件．By using a continuation theorem based on Gaines and Mawhin＇s coincidence degree, the authors study the global exisence of ：positive periodic solutions of a delayed predator-prey system with Holling II type response and stage structure for predator. A set of easily verifiable sufficient conditions is obtained, which improves some known results. Also, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the global attractivity of the positive periodic solution are obtained.

关 键 词：捕食者-食饵系统 HOLLING Ⅱ类功能性反应 阶段结构 重合度 周期解 

分 类 号：O175.14[理学—数学]