| 一类捕食者-食饵模型的稳定性及Hopf分支 |
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| 引用本文： | 冯光辉,王玲书,米香云.一类捕食者-食饵模型的稳定性及Hopf分支[J].数学的实践与认识,2012,42(1):122-126. |
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| 作者姓名： | 冯光辉 王玲书 米香云 |
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| 作者单位： | 1. 军械工程学院基础部,河北石家庄,050003
2. 河北经贸大学数学与统计学学院,河北石家庄,050061 |
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| 基金项目： | 河北省科技厅资助项目(11457201D-39);河北省自然科学基金(A2011207003);国家自然科学基金(11101117) |
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| 摘 要： | 研究一类具有时滞和阶段结构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.利用规范型和中心流形定理,给出了确定Hopf分支方向和分支周期解的稳定性的计算公式.
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| 关 键 词： | 时滞 阶段结构 稳定性 Hopf分支 |
Stability and Hopf Bifurcation of a Predator-Prey Model |
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| FENG Guang-hui
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WANG Ling-shu
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MI Xiang-yun.Stability and Hopf Bifurcation of a Predator-Prey Model[J].Mathematics in Practice and Theory,2012,42(1):122-126. |
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| Authors: | FENG Guang-hui WANG Ling-shu MI Xiang-yun |
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| Institution: | 1.Department of Basic Courses,Mechanical Engineering College,Shijiazhuang 050003,China) (2.School of Mathematics and Statistics,Hebei University of Economics & Business,Shijiazhuang 050061, China) |
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| Abstract: | The stability and Hopf bifurcations of a predator-prey model with time delay and stage structure is investigated.By choosing time delay as the parameter,the stability of a positive equilibrium and the existence of Hopf bifurcations are established.Formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. |
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| Keywords: | time delay stage structure stability Hopf bifurcation |
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