一类具有相互干扰的Leslie捕食与被捕食系统的定性分析  

Qualitative Analysis of A Leslie Predator-Prey System with Mutual Interference

作　　者：张凤[1,2] 陈文成[1] 张永明 

机构地区：[1]山东农业大学数学系,山东泰安271018 [2]山东科技大学数学系,山东青岛266590

出　　处：《生物数学学报》2014年第1期169-173,共5页Journal of Biomathematics

基　　金：国家自然科学基金资助项目(11071238)

摘　　要：用定性分析的方法研究了一类具有相互干扰的Leslie捕食与被捕食周期系统的全局性质,讨论了系统的持久性以及周期解的存在唯一性,并且给出了该系统持久性的充分条件以及存在全局渐近稳定正周期解的充分条件.This thesis is devoted to study the persistence,of predator-prey system with mutual interference and the existence and the uniqueness of periodic solution of it.As we aE know,the predator-prey model was declared by Leslie.Based on it,Hassell proposed the Leslie predator-prey model with mutual interference.An improved Leslie-prey model with mutual interference is considered in this thesis,and it is better for the practical researches in the ecological system,furthermore,a sufficient condition of the persistent system is obtained.At the same time existence and uniqueness of positive periodic solution of system is analyzed,based on it,two sufficient conditions of the existence and the uniqueness of positive periodic solution are obtained.

关 键 词：Leslie捕食与被捕食模型 持久性 正周期解 全局渐近稳定 

分 类 号：Q145.1[生物学—生态学]