| 一个在无穷远点分支出6个极限环的三次多项式系统 |
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| 引用本文： | 黄文韬,刘一戎. 一个在无穷远点分支出6个极限环的三次多项式系统[J]. 中南大学学报(自然科学版), 2004, 35(4): 690-693 |
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| 作者姓名： | 黄文韬 刘一戎 |
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| 作者单位： | 1. 中南大学,数学科学与计算技术学院,湖南,长沙,410083;桂林电子工业学院,计算科学与数学系,广西,桂林,541005
2. 中南大学,数学科学与计算技术学院,湖南,长沙,410083 |
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| 基金项目： | 国家自然科学基金，广西教育厅科研项目 |
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| 摘 要： | 研究了一类三次系统无穷远点的极限环分支问题.对一类三次系统给出了计算无穷远点奇点量的递推公式,并在计算机上用计算机代数系统Mathematica推导出该系统无穷远点的前6个奇点量,进而导出了无穷远点成为中心和最高阶细焦点的条件,在此基础上得到了一个三次系统在无穷远点分支出6个极限环的实例,指出了极限环的精确位置.
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| 关 键 词： | 三次多项式系统 奇点量 无穷远点 极限环分支 |
| 文章编号： | 1672-7207(2004)04-0690-04 |
| 修稿时间： | 2003-11-10 |
A cubic polynomial system with six limit cycles at infinity |
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| HUANG Wen-tao. A cubic polynomial system with six limit cycles at infinity[J]. Journal of Central South University:Science and Technology, 2004, 35(4): 690-693 |
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| Authors: | HUANG Wen-tao |
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| Affiliation: | HUANG Wen-tao~ |
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| Abstract: | The bifurcation of limit cycles at infinity for a class of cubic polynomial systems was studied in the paper. A recursive formula is derived to compute singular point values at infinity. (Using) the recursive formula and computer algebra system-Mathematica, the first six singular point values at infinity of the system are given. The conditions for infinity to be a center and the highest degree fine focus are derived, respectively. A cubic system that bifurcates six limit cycles from infinity is obtained. The exact positions of these limit cycles are also pointed out. |
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| Keywords: | cubic polynomial system singular point value infinity bifurcation of limit cycles |
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