| 一类Z8-等变对称七次系统的极限环分枝 |
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| 引用本文： | 杜超雄.一类Z8-等变对称七次系统的极限环分枝[J].邵阳学院学报(自然科学版),2009,6(1):1-7. |
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| 作者姓名： | 杜超雄 |
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| 作者单位： | 中南大学,数学与计算技术学院,湖南,长沙,410083 |
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| 基金项目： | 国家自然科学基金，湖南省自然科学基金，湖南省教育厅科研项目 |
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| 摘 要： | 本文研究了一类Z8等变对称的七次微分扰动系统，在个人计算机上推导出八个拓扑结构相同的焦点中其中一个的前5个奇点量，进而得出其前5阶焦点量，并得出由八个拓扑结构相同的焦点共可在一定条件下分支出40个极限环的好的结论，同时找出了它的分支条件及极限环稳定性的判断条件．
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| 关 键 词： | Z8-等变对称系统 焦点量 极限环分支 |
The Bifurcation of Limit Cycles for a Class of Z8-Equivariant Seventh Degree System |
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| DU Chao-xiong.The Bifurcation of Limit Cycles for a Class of Z8-Equivariant Seventh Degree System[J].Journal of Shaoyang University:Science and Technology,2009,6(1):1-7. |
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| Authors: | DU Chao-xiong |
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| Institution: | DU Chao-xiong (School of Mathematics,Central South University, Changsha, Hunan,410083 ) |
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| Abstract: | A class of Zs-equivariant seventh degree system is investigated and its first five order critical point values are given in personal computer, we discuss the bifurcation behavior of limit cycles ,show that there are eight fine foci of five order and five limit cycles can bifurcate from each. So 40 small amplitude limit cycles can bifurcate from the seventh degree Z8-equivariant system under a certain condition.At the same time,the bifurcation condition and stability condition of limit cycles are obtained. |
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| Keywords: | Z8-equivariant system focal point value limit cycle bifurcation |
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