| 一类平面七次多项式系统赤道环的稳定性与极限环分支 |
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| 引用本文： | 陈海波,罗交晚.一类平面七次多项式系统赤道环的稳定性与极限环分支[J].应用数学,2002,15(2):22-25. |
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| 作者姓名： | 陈海波 罗交晚 |
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| 作者单位： | 中南大学数学系,湖南,长沙,410075 |
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| 摘 要： | 本文研究一类平面七次多项式系统赤道环的稳定性和极限环分支，给出了系统的前12个奇点量公式，可积性条件及在赤道附近存在3个极限环的条件，较为精细地指出了极限环的存在位置。
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| 关 键 词： | 多项式系统 赤道环 稳定性 可积性 极限环分支 奇点量 |
| 文章编号： | 1001-9847(2002)02-0022-04 |
| 修稿时间： | 2001年10月28 |
Stability and Bifurcation of Limit Cycles of the Equator in a Class of Septic Polynomial Systems |
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| CHEN Hai-bo,LUO Jiao-wan.Stability and Bifurcation of Limit Cycles of the Equator in a Class of Septic Polynomial Systems[J].Mathematica Applicata,2002,15(2):22-25. |
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| Authors: | CHEN Hai-bo LUO Jiao-wan |
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| Abstract: | In this paper, we study the appearance of limit cycles from the equator in a class of septic polynomial vector fields with no singular points at infinity and the stability of the equator of the system. We reach an expression of the first 12 quantities of singular point of the system and give integrability condition and the condition, which allows the appearance of three limit cycles in the neighborhood of the equator. |
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| Keywords: | Cubic system Quantities at infinity Bifurcation of limit cycles |
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