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| 一类具有三次代数曲线同异宿环的三次系统 | |
| 引用本文： | 叶星旸,陈永雪,李学鹏.一类具有三次代数曲线同异宿环的三次系统[J].徐州师范大学学报(自然科学版),2008,26(2):101-106. |
| 作者姓名： | 叶星旸 陈永雪 李学鹏 |
| 作者单位： | 1. 集美大学,理学院,福建,厦门,361021 2. 福建农林大学,计算机与信息学院,福建,福州,350002 3. 福建师范大学,数学与计算机科学学院,福建,福州,350007 |
| 摘 要： | 通过分析一类三次系统的不变三次代数曲线的性质,得出该三次曲线及一条不变直线能同时构成系统同宿环和异宿环,进而构造双参数的旋转向量场使同异宿环各自破裂而产生极限环. |
| 关 键 词： | 三次系统 同宿环 异宿环 极限环 |
Cubic System with Homoclinic and Heteroclinic Cycles Formed by the Invariant Cubic Curve Associated with an Invariant Line |
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| YE Xing-yang,CHEN Yong-xue,LI Xue-peng.Cubic System with Homoclinic and Heteroclinic Cycles Formed by the Invariant Cubic Curve Associated with an Invariant Line[J].Journal of Xuzhou Normal University(Natural Science Edition),2008,26(2):101-106. | |
| Authors: | YE Xing-yang CHEN Yong-xue LI Xue-peng |
| Institution: | YE Xing-yang,CHEN Yong-xue,LI Xue-peng (1.College of Science,Jimei University,Xiamen,Fujian,361021;2.College of Computer ＆ Information,Fujian Agriculture ＆ Forestry University,Fuzhou,Fujian,350002;3.College of Mathematics ＆ Computer Science,Fujian Normal University,Fuzhou,Fujian,350007) |
| Abstract: | An invariant cubic curve of a cubic system is first presented in this paper. By studying the properties of the invariant curve in detail, it is concluded that the invariant cubic curve together with an invariant line can constitute a homoclinic cycle and a heteroclinic cycle of the cubic system, which has not been seen before. Finally, a two-parameter rotated vector field is constructed to bifurcate limit cycles from the homoclinic and heteroclinic cycles, respectively. |
| Keywords: | cubic system homoclinic cycle heteroclinic cycle limit cycle |
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