| 一类具有阶段结构和时滞的捕食模型的稳定性及Hopf分支(英文) |
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| 引用本文： | 王玲书.一类具有阶段结构和时滞的捕食模型的稳定性及Hopf分支(英文)[J].应用数学,2012,25(1):131-139. |
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| 作者姓名： | 王玲书 |
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| 作者单位： | 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： | Supported by the National Natural Science Foundation of China(11101117,11071254) |
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| 摘 要： | 研究一类具有阶段结构和时滞的捕食模型.通过特征方程分别分析了正平衡点和边界平衡点的局部稳定性,到了系统Hopf分支存在的充分条件.通过规范型理论和中心流型定理,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： | 捕食模型 阶段结构 时滞 稳定性 Hopf分支 |
Stability and Hopf Bifurcation in a Predator-prey Model with Stage Structure and Time Delay |
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| WANG Lingshu.Stability and Hopf Bifurcation in a Predator-prey Model with Stage Structure and Time Delay[J].Mathematica Applicata,2012,25(1):131-139. |
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| Authors: | WANG Lingshu |
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| Institution: | WANG Lingshu(School of Mathematics and Statistics,Hebei University of Economics & Business,Shijiazhuang 050061,China) |
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| Abstract: | A predator-prey system with time delay due to the gestation of the predator and stage structure for both the predator and the prey is proposed and investigated.By analyzing the corresponding characteristic equations,the stability of a positive equilibrium and two boundary equilibria of the system is discussed,respectively.Further,the existence of Hopf bifurcations at the positive equilibrium is also studied.By using the normal form theory and center manifold theorem,formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given. |
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| Keywords: | Predator-prey model Stage structure Time delay Stability Hopf bifur cation |
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