| 一类三次系统无穷远点的中心条件与赤道极限环分支 |
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| 引用本文： | 张齐,刘一戎.一类三次系统无穷远点的中心条件与赤道极限环分支[J].工程数学学报,2006,23(6):984-988. |
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| 作者姓名： | 张齐 刘一戎 |
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| 作者单位： | 中南大学数学科学与计算技术学院,长沙,410075;中南大学数学科学与计算技术学院,长沙,410075 |
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| 摘 要： | 本文研究了一类三次系统无穷远点的中心条件与赤道极限环分枝问题。通过将实平面系统转化为复系统研究,给出了计算无穷远点奇点量的递推公式,并在计算机上用Mathematica推导出该系统无穷远点前七个无穷远点奇点量,进一步导出了无穷远点成为中心的条件和七阶细焦点的条件,得到了三次系统无穷远点分支出七个极限环的一个实例。
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| 关 键 词： | 三次多项式系统 无穷远点 奇点量 极限环分枝 |
| 文章编号： | 1005-3085(2006)06-0984-05 |
| 收稿时间： | 2004-11-12 |
| 修稿时间： | 2004年11月12 |
Center Conditions and Bifurcation of Limit Cycles from the Equator for a Class of Cubic Polynomial Differential System |
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| ZHANG Qi,LIU Yi-rong.Center Conditions and Bifurcation of Limit Cycles from the Equator for a Class of Cubic Polynomial Differential System[J].Chinese Journal of Engineering Mathematics,2006,23(6):984-988. |
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| Authors: | ZHANG Qi LIU Yi-rong |
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| Affiliation: | School of Mathematical Science and Computing Technology Central South University, Changsha 410075 |
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| Abstract: | Studied in this paper are center conditions and bifurcation of limit cycles from the equator for a class of cubic polynomial system.By converting the real planar system into complex system,the recursion formula for the computation of singular quantities at infinity are given,and,with Mathemat- ica,the first 7 singular point quantities at infinity are deduced.At the same time,the condition for the infinity to be a center and 7 degree fine focus are derived,respectively.A cubic system that bifurcates 7 limit cycles from infinity is obtained. |
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| Keywords: | cubic polynomial system infinity singular point quantity bifurcation of limit cycles |
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