| 一类具有时滞和常数收获率的比率型功能性反应的捕食-被捕食模型的稳定性与Hopf分支 |
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| 引用本文： | 薛立波,徐瑞.一类具有时滞和常数收获率的比率型功能性反应的捕食-被捕食模型的稳定性与Hopf分支[J].军械工程学院学报,2008,20(6):73-78. |
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| 作者姓名： | 薛立波 徐瑞 |
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| 作者单位： | 军械工程学院基础部,河北石家庄050003 |
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| 基金项目： | 国家自然科学基金项目(10671209) |
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| 摘 要： | 研究一类具有时滞和常数收获率的比率型功能性反应的捕食—被捕食模型。首先,分析了模型奇点的类型,研究了正平衡点的局部稳定性以及Hopf分支的存在性;然后应用中心流形和规范型理论,得到了关于确定Hopf分支方向和分支周期解稳定性的计算公式;最后,应用Matlab软件对所得理论结果进行了数值模拟。
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| 关 键 词： | 时滞 收获率 稳定性 Hopf分支 周期解 |
Stability and Bifurcation in a Ratio-Dependent Predator-Prey System with Time Delay and Harvesting |
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| XUE Li-bo,XU Rui.Stability and Bifurcation in a Ratio-Dependent Predator-Prey System with Time Delay and Harvesting[J].Journal of Ordnance Engineering College,2008,20(6):73-78. |
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| Authors: | XUE Li-bo XU Rui |
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| Institution: | XUE Li-bo,XU Rui(Department of Basic Courses,Ordnance Engineering College,Shijiazhuang 050003,China) |
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| Abstract: | A ratio-dependent predator-prey system with time delay and constant rate harvesting is investigated.First,we discuss the types of the two equilibria,and consider the local stability of a positive equilibrium and the existence of Hopf bifurcations.Then,by using the normal form theory and center manifold reduction,we derive explicit formula determining the properties of bifurcating periodic solutions.Finally,numerical results are given to support the theoretical predictions. |
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| Keywords: | time delay harvesting stability Hopf bifurcation periodic solution |
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