一个具有阶段结构和Holling-Ⅱ型功能反应的捕食者-食饵模型的全局稳定性(英文)  

Global Dynamics of a Predator-prey Model with Stage Structure and Holling Type-Ⅱ Functional Response

作　　者：王玲书[1] 冯光辉[2] 

机构地区：[1]河北经贸大学数学与统计学学院,河北石家庄050061 [2]军械工程学院基础部数学教研室,河北石家庄050003

出　　处：《应用数学》2013年第4期765-773,共9页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China (11071254,11101117)

摘　　要：研究一个具有Holling-Ⅱ型功能反应的捕食者-食饵均具有阶段结构的捕食者-食饵模型的稳定性.通过分析特征方程,讨论该模型非负平衡点的局部稳定性,并得到系统持续生存的充分条件.通过构造适当的Lyapunov泛函,运用LaSalle不变集原理,讨论该模型的非负平衡点的全局稳定性.In this paper,a predator-prey model with Holling type II functional response and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is addressed. The sufficient condition for the permanence of the system is derived. By using Lyapunov functions and the LaSalle invariance principle,the global stability of each of feasible equilibria of the system is studied.

关 键 词：阶段结构 LaSalle不变集原理 全局稳定性 

分 类 号：O175.1[理学—数学]