| 具有四点异宿环和同宿环共存的平面五次多项式系统 |
| |
| 引用本文： | 陈永雪,叶星旸,李学鹏.具有四点异宿环和同宿环共存的平面五次多项式系统[J].福建师范大学学报(自然科学版),2006,22(1):29-33,36. |
| |
| 作者姓名： | 陈永雪 叶星旸 李学鹏 |
| |
| 作者单位： | 福建师范大学数学与计算机科学学院,福建,福州,350007 |
| |
| 基金项目： | 福建省教育厅基金资助项目（JA05204） |
| |
| 摘 要： | 给出一平面五次多项式微分系统存在五次代数不变曲线的条件．经分析，获得系统在一定条件下同时存在一个四点异宿环和一个同宿环（它们内部均只含一个焦点）．进一步根据旋转向量场理论研究了它们各自分支出极限环的条件．
|
| 关 键 词： | 平面微分系统 代数不变曲线 异宿环 同宿环 极限环 |
| 文章编号： | 1000-5277（2006）01-0029-05 |
| 收稿时间： | 2005-04-10 |
| 修稿时间： | 2005-04-10 |
The Planar Quintic Polynomial Systems with a Four-point Heteroclinic Cycle and a Homoclinic Cycle Coexist |
| |
| CHEN Yong-xue,YE Xing-yang,LI Xue-peng.The Planar Quintic Polynomial Systems with a Four-point Heteroclinic Cycle and a Homoclinic Cycle Coexist[J].Journal of Fujian Teachers University(Natural Science),2006,22(1):29-33,36. |
| |
| Authors: | CHEN Yong-xue YE Xing-yang LI Xue-peng |
| |
| Institution: | School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China |
| |
| Abstract: | The conditions of one family of planar quintic polynomial differential system which(possesses) a quintic algebraic invariant curve are presented.By analysis,the system has a heteroclinic cycle connecting four saddle points and a homoclinic cycle under certain conditions(their inner unique sigular point is a focus,respectively).Then the rotated vector field is constructed to bifurcate cycles from the homoclinic and heteroclinic cycles,respectively. |
| |
| Keywords: | planar differential system algebraic invariant curve heteroclinic homoclinic limit cycle |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
