| 一类三次平面自治系统的异宿环分支 |
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| 引用本文： | 陈方芳.一类三次平面自治系统的异宿环分支[J].常熟理工学院学报,2008,22(2):26-30. |
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| 作者姓名： | 陈方芳 |
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| 作者单位： | 黎明大学,数学系,福建,泉州,362000 |
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| 摘 要： | 对一类给定的三次多项式系统，寻找该系统的一类特殊代数不变曲线，得到这些代数不变曲线为异宿轨线的条件；并分析该系统的奇点．讨论了闭轨线的存在性问题，得到系统在相平面的单位圆盘叉上的全局结构，从而得出相图随参数变化的情况．
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| 关 键 词： | 奇点 异宿环 Dulac函数 Poincare变换 |
| 文章编号： | 1008-2794(2008)02-0026-05 |
| 修稿时间： | 2007年8月23日 |
The Bifurcation of the Heteroelinic Loop in a Cubic Autonomous System |
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| CHEN Fang-fang.The Bifurcation of the Heteroelinic Loop in a Cubic Autonomous System[J].Journal of Changshu Institute of Technology,2008,22(2):26-30. |
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| Authors: | CHEN Fang-fang |
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| Institution: | CHEN Fang-fang ( Department of Mathematics Liming University, Quanzhou 362000, China) |
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| Abstract: | According to a plane autonomous system,this paper considers seeking its a special algebra invariant curve to get the condition of these curves being heteroelinic orbits.Then by way of the analysis of the singularities and the discussion about the existence of a closed-orbit,it obtains the global topological structure of phase-portraits of this system.Finally,it obtains the variation of the phase-portraits with the varying of the parameter. |
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| Keywords: | singularity heteroelinic loop the Dulac function the Poincare inversion |
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