| 一类E33系统的Hopf分支和原点为中心时的全局结构 |
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| 引用本文： | 刘磊,何西兵.一类E33系统的Hopf分支和原点为中心时的全局结构[J].宝鸡文理学院学报(自然科学版),2009,29(2):19-21. |
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| 作者姓名： | 刘磊 何西兵 |
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| 作者单位： | 商丘师范学院,数学系,河南,商丘,476000;宝鸡亚太专修学院,基础教研组,陕西,宝鸡,721302 |
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| 基金项目： | 陕西省自然科学基金资助项目(2003A07) |
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| 摘 要： | 目的研究了一类E33系统的定性性质。方法运用定性理论和平面系统的分支理论。结果给出了原点O(0,0)为全局中心时的所有可能的全局结构和产生Hopf分支的充分条件。结论得到了关于此类三次系统的比较完整的结果。
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| 关 键 词： | 全局中心 全局结构 Hopf分支 |
The Hopf bifurcation and global structure when O(0,0) is a center of a class of cubic systems |
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| LIU Lei,HE Xi-bing.The Hopf bifurcation and global structure when O(0,0) is a center of a class of cubic systems[J].Journal of Baoji College of Arts and Science(Natural Science Edition),2009,29(2):19-21. |
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| Authors: | LIU Lei HE Xi-bing |
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| Institution: | 1.Department of Mathematics;Shangqiu Normal University;Shangqiu 476000;Henan;China;2.Basic Teaching and Research Group;Baoji Yatai Specialized School;Baoji 721302;Shaanxi;China |
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| Abstract: | Aim To research the qualitative property of a class of cubic system.Methods The qualitative theories and bifurcation theory of planar system are used to study the property.Results All the possible global structures are obtained when O(0,0) is a center;meanwhile,the sufficient conditions for the system to generate the Hopf bifurcation are given.Conclusion The relative systematic results on this class of cubic system are obtained. |
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| Keywords: | global center global structures Hopf bifurcation |
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