| 多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支 |
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| 引用本文： | 宋永利,韩茂安,魏俊杰.多时滞捕食-食饵系统正平衡点的稳定性及全局Hopf分支[J].数学年刊A辑(中文版),2004(6). |
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| 作者姓名： | 宋永利 韩茂安 魏俊杰 |
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| 作者单位： | 上海交通大学数学系，上海交通大学数学系，哈尔滨工业大学数学系 上海 200240，上海 200240，哈尔滨 150001 |
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| 基金项目： | 国家自然科学基金(No.10371072)资助的项目. |
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| 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.
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| 关 键 词： | 时滞 稳定性 局部Hopf分支 全局Hopf分支 |
STABILITY AND GLOBAL HOPF BIFURCATION FOR A PREDATOR-PREY MODEL WITH TWO DELAYS |
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| SONG Yongli HAN Maoan WEI Junjie.STABILITY AND GLOBAL HOPF BIFURCATION FOR A PREDATOR-PREY MODEL WITH TWO DELAYS[J].Chinese Annals of Mathematics,2004(6). |
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| Authors: | SONG Yongli HAN Maoan WEI Junjie |
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| Institution: | SONG Yongli HAN Maoan WEI Junjie Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China.Department of Mathematics,Shanghai Jiaotong University,Shanghai 200240,China. Department of mathematics,Haerbin Institute of Technology,Harbin 150001,China. |
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| Abstract: | 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. |
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| Keywords: | Delay Stability Local Hopf bifurcation Global Hopf bifurcation |
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