| 一类高维生物数学模型小扰动下的Hopf分支 |
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| 引用本文： | 袁晓凤,郭瑞海,吴云华.一类高维生物数学模型小扰动下的Hopf分支[J].数学物理学报(A辑),1999,19(2):189-195. |
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| 作者姓名： | 袁晓凤 郭瑞海 吴云华 |
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| 作者单位： | 中国科学院成都计算所数理室!成都610041(袁晓凤，郭瑞海)，西南民族学院数学系!成都610041(吴云华) |
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| 摘 要： | 讨论一类六维生物数学模型，在［１，２］的基础上，进一步考虑生物种群之间的相互作用，引进扰动项，研究了中心流形及Ｈｏｐｆ分支问题．利用计算机代数符号软件计算了中心流形，得到了产生Ｈｏｐｆ分支的判定条件，并给出了数值算例，所用机器证明的思想方法可广泛运用于类似复杂生物数学模型的研究．
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| 关 键 词： | 定性理论 平衡点 中心流形 Hopf分支 计算机代数 |
Hopf Bifurcation in the Multi-Dimension Biomathematics Model under Small Perturbation |
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| Yuan Xiaofeng,Guo Ruihai,Wu Yunhua.Hopf Bifurcation in the Multi-Dimension Biomathematics Model under Small Perturbation[J].Acta Mathematica Scientia,1999,19(2):189-195. |
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| Authors: | Yuan Xiaofeng Guo Ruihai Wu Yunhua |
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| Abstract: | The six-dimension biomathematics model is studied. Interactions among the microbes are considered and the model in 1] 2] is improved. The problems on center manifold and Hop f bifurcation a re discussed. The center manifold and the criterion quantity of Hopf bifurcation are computed by using symbolic software based on computer algebra. The numeracal example are given. The idea and method on Automated Theorem proving can be applied to various complex biodynamical systems. |
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| Keywords: | Qualitative theory Equilibrium points Center manifold Hopf bifurcation Computer algebra |
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