| 一类具有时滞和阶段结构的捕食模型及其Hopf分支 |
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| 引用本文： | 冯光辉,王玲书.一类具有时滞和阶段结构的捕食模型及其Hopf分支[J].吉林林学院学报,2010(1):13-18. |
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| 作者姓名： | 冯光辉 王玲书 |
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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： | 基金项目：河北省教育厅科学研究计划项目（No.2009114）. |
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| 摘 要： | 研究一类具有时滞、阶段结构和HollingII型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局部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 |
Hopf Bifurcation of a Predator-Prey Model with Time Delay and Stage Structure |
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| Authors: | FENG Guang-hui WANG LIng-shu |
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| Institution: | 1. Department of Basic Course, 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 bifurcation of a predator-prey model with time delay, stage structure and Holling I functional response are investigated. Choosing time delay as the parameter, the sufficient conditions of the stability of a positive equalibrium and the existence of Hopf bifurcation 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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