一类具Michaelis-Menten功能反应的时滞比率依赖捕食-被捕食模型的一致持久性和周期解  

Uniform persistence and periodic solution of a delayed ratio-dependent predator-prey model with Michaelis-Menten functional response

作　　者：刘华祥[1] 曾广洪[2] 

机构地区：[1]广东海洋大学理学院数学系,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）》2014年第1期24-30,44,共8页Journal of Nanchang University(Natural Science)

基　　金：广东海洋大学科研资助项目(0612163);江西省教育厅科学技术研究项目(GJJ13219)

摘　　要：研究一类具时变参数的周期非自治时滞比率依赖捕食-被捕食模型的持久性和周期解。应用微分方程的比较定理证明了系统在一定条件下是一致持久的;运用叠合度理论中的延拓定理,建立了保证该系统至少存在1个正周期解的便于验证的充分条件。This study was designed to verify a periodic ratio-dependent predator-prey model with Michaelis-Menten functional response and variable time delays. By using the comparison theorem of differential equations,we established sufficient conditions for the uniform persistence of the system. By using the continuation theorem of coincidence degree theory,an easily verifiable sufficient condition was obtained for the existence of positive periodic solutions of the system.

关 键 词：比率依赖 时滞 捕食-被捕食 一致持久性 正周期解 

分 类 号：O175.13[理学—数学]