| 一类具有时滞和Holling Ⅲ型功能性反应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.一类具有时滞和Holling Ⅲ型功能性反应的捕食模型的稳定性和Hopf分支[J].数学的实践与认识,2008,38(24). |
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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;军械工程学院应用数学研究所,河北,石家庄,050003
2. 军械工程学院应用数学研究所,河北,石家庄,050003 |
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| 基金项目： | 国家自然科学基金资助项目
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| 摘 要： | 研究一类具有时滞和Holling Ⅲ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Hopf分支存在的充分条件,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 Holling Ⅲ型功能性反应 稳定性 Hopf分支 |
Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Holling Type-Ⅲ Functional Response |
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| WANG Ling-shu,XU Rui,FENG Guang-hui.Stability and Hopf Bifurcation of a Predator-Prey Model with Time Delay and Holling Type-Ⅲ Functional Response[J].Mathematics in Practice and Theory,2008,38(24). |
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| Authors: | WANG Ling-shu XU Rui FENG Guang-hui |
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| Institution: | 1.School of Mathematics and Statistics;Hebei University of Economics & Business;Shijiazhuang Hebei 050061;China;2.Institute of Applied Mathematics;Mechanical Engineering College;Shijiazhuang Hebei 050003;China |
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| Abstract: | A predator-prey model with time delay and Holling type-Ⅲ functional response is investigated.By choosing time delay as the bifurcation parameter and analyzing the associated characteristic equation of the linearized system,the linear stability of the system is investigated and Hopf bifurcations are established.In particular,the 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 Holling type-Ⅲ functional response stability Hopf bifurcation |
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