| 一类具有时滞的捕食模型的稳定性和Hopf分支 |
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| 引用本文： | 王玲书,徐瑞,冯光辉.一类具有时滞的捕食模型的稳定性和Hopf分支[J].数学的实践与认识,2010,40(5). |
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| 作者姓名： | 王玲书 徐瑞 冯光辉 |
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| 作者单位： | 1. 河北经贸大学数学与统计学学院,河北石家庄050061;军械工程学院基础部数学教研室,河北石家庄050003
2. 军械工程学院基础部数学教研室,河北石家庄,050003 |
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| 基金项目： | 河北省教育厅科学研究计划项目(2009114); 国家自然科学基金(10926064) |
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| 摘 要： | 研究一类具有时滞和Beddington-DeAngelis功能性反应的捕食模型的稳定性和Hopf分支.以滞量为参数,得到了系统正平衡点的稳定性和Hopf分支存在的充分条件.应用一般泛函微分方程的度理论,研究了该系统的全局Hopf分支的存在性.
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| 关 键 词： | 时滞 Beddington-DeAngelis功能性反应 稳定性 Hopf分支 |
Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay |
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| WANG Ling-shu,XU Rui,FENG Guang-hui.Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay[J].Mathematics in Practice and Theory,2010,40(5). |
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| Authors: | WANG Ling-shu XU Rui FENG Guang-hui |
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| Institution: | WANG Ling-shu~(1,2),XU Rui~2,FENG Guang-hui~2 (1.School of Mathematics , Statistics,Hebei University of Economics & Business,Shijiazhuang 050061,China) (2.Department of Mathematics,Mechanical Engineering College,Shijiazhuang 050003,China) |
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| Abstract: | A predator-prey model with time delay and Beddington-DeAngelis functional response is investigated.By choosing time delay as the parameter,the sufficient conditions of the stability of the positive equalibrium and the existnce of Hopf bifurcation are established. Based on the degree theory of general functional differential equations,the global existence of periodic solutions is discussed. |
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| Keywords: | time delay Beddington-DeAngelis functional response stability Hopf bifurcation |
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