| 一类三次系统的极限环个数与奇点分支 |
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| 引用本文： | 谢向东,陈凤德. 一类三次系统的极限环个数与奇点分支[J]. 系统科学与数学, 2005, 25(4): 414-422 |
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| 作者姓名： | 谢向东 陈凤德 |
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| 作者单位： | 1. 宁德师范高等专科学校,宁德,352100;漳州师范学院数学系,漳州,363000
2. 福州大学数学与计算机科学学院,福州,350002 |
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| 基金项目： | 国家自然科学基金数学天元基金(10426010)福建省自然科学基金(20511052)福建省教育厅科研基金宁德师专重点科研基金 |
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| 摘 要： | 给出二次系统I的一类相伴系统在奇点O(0,0)的焦点量公式,证明了O至多为2阶细焦点,δlmn=0时系统在O外围至多有一个极限环,从而说明了系统在细焦点外围至多有一个极限环。最后给出了各个奇点的分支情况及几何特征。
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| 关 键 词： | 相伴系统 三次系统 分支 极限环 唯一性 |
| 修稿时间： | 2003-04-15 |
THE NUMBER AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF CUBIC SYSTEMS |
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| Xie Xiangdong,Chen Fengde. THE NUMBER AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF CUBIC SYSTEMS[J]. Journal of Systems Science and Mathematical Sciences, 2005, 25(4): 414-422 |
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| Authors: | Xie Xiangdong Chen Fengde |
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| Affiliation: | (1)Ningde Teachers College, Ningde, $352100$; Department of Mathematics, Zhangzhou Normal College, Zhangzhou, 363000;(2)Fuzhou Univerisity,Fuzhou 350002 |
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| Abstract: | This paper gives the focus values of each order at$O(0,0)$ for a class of accompanying system of the quadratic differential system I, and provesthat the system with $de lmn=0 $ has at most one limit cycle surrounding $O$, whichmeans that the system has at most one limit cycle surrounding weak focus. Finally thegeometric characteristics of all singular points are given. |
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| Keywords: | Accompanying system cubic system bifurcation limit cycle uniqueness. |
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