| 具有时滞的比率型Chemostat模型的全局稳定性 |
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| 引用本文： | 张晓,徐瑞,薛立波.具有时滞的比率型Chemostat模型的全局稳定性[J].军械工程学院学报,2009,21(3):75-78. |
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| 作者姓名： | 张晓 徐瑞 薛立波 |
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| 作者单位： | 军械工程学院基础部; |
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| 基金项目： | 国家自然科学基金(10671209) |
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| 摘 要： | 研究一类具有时滞的比率型功能性反应的Chemostat模型。研究了模型的边界平衡点和正平衡点的局部稳定性以及Hopf分支的存在性;利用比较定理证明了边界平衡点的全局稳定性;通过构造Liapunov泛函给出了保证系统正平衡点全局稳定的充分条件;并通过数值模拟验证了理论结果。
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| 关 键 词： | 时滞 比率 Chemostat 全局稳定性 |
Global Stability for Ratio-dependent Chemostat Model with Time Delay |
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| ZHANG Xiao,XU Rui,XUE Li-bo.Global Stability for Ratio-dependent Chemostat Model with Time Delay[J].Journal of Ordnance Engineering College,2009,21(3):75-78. |
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| Authors: | ZHANG Xiao XU Rui XUE Li-bo |
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| Institution: | Department of Basic Courses;Ordnance Engineering College;Shijiazhuang 050003;China |
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| Abstract: | A delayed Chemostat model which is ratio-dependent is investigated.The local stability of bound equilibrium and positive equilibrium are researched.The existence of Hopf bifurcations is established.By using the comparison argument,the sufficient conditions are derived for the global stability of the boundary equilibrium of the model.By working out a suitable Liapunov functional,sufficient conditions are derived for the global asymptotic stability of the positive equilibrium of the model.Finally,numerical si... |
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| Keywords: | time delay ratio-dependent chemostat global stability |
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