多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支  

STABILITY AND GLOBAL HOPF BIFURCATION FOR A PREDATOR-PREY MODEL WITH TWO DELAYS

作　　者：宋永利[1] 韩茂安[1] 魏俊杰[2] 

机构地区：[1]上海交通大学数学系,上海200240 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《数学年刊（A辑）》2004年第6期783-790,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10371072)资助的项目.

摘　　要：本文首先用Cooke等人建立的关于超越函数的零点分布定理,研究了一类多时滞捕食-食饵系统正平衡点的稳定性及局部Hopf分支,在此基础上再结合吴建宏等人用等变拓扑度理论建立起的一般泛函微分方程的全局Hopf分支定理,进一步研究了该系统的全局Hopf分支.This paper considers the stability and local Hopf bifurcation for a delayed Predator-Prey model using the basic theorem on zeros of general transcendental function, which was established by Cooke etc. Furthermore, based on the global Hopf bifurcation theorem for general functional differential equations, which was established by Wu J. etc. using degree theory methods, the existence of global Hopf bifurcation is investigated.

关 键 词：时滞 稳定性 局部Hopf分支 全局HOPF分支 

分 类 号：O177.91[理学—数学]