具有HollingⅣ类功能反应的三维顺环捕食者—食饵模型  

A Three-Species Clockwise Chain Predator-prey Model with Holling Ⅳ Functional Response

作　　者：刘会民[1] 刘兵[1] 刘双[1] 

机构地区：[1]鞍山师范学院数学系,辽宁鞍山114005

出　　处：《生物数学学报》2004年第4期445-452,共8页Journal of Biomathematics

基　　金：国家自然科学基金(40272111)

摘　　要：考虑具有Holling Ⅳ类功能反应三维顺环捕食者-食饵系统。利用常微分方程比较定理及Liapunov函数方法，得到了该系统持久性的充分条件，并且对于周期系统在一定条件下，系统存在唯一一个全局渐进稳定的周期正解。最后讨论了概周期解现象，得出了概周期正解的唯一存在性和全局渐进稳定性的充分条件。In this paper, we consider a three-species clockwise chain predator-prey system with Holling Ⅳ functional response. Some sufficient conditions which guarantee the permanence of the system are determined by using comparison theory and Liapunov function of ordinary differential equation. Moreover, for the periodic system, it is proved that under certain conditions there exists a unique positive periodic solution which is globally asymptotically stable. Finally, we discuss almost periodic phenomena, and obtain some sufficient conditions which assure the unique existence and globally asymptotic stability of almost positive periodic solution.

关 键 词：充分条件 全局渐进稳定性 唯一 Liapunov函数方法 周期系统 功能反应 概周期解 食饵 捕食者 周期正解 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]