| 摘要: |
| 用一个变换把系统无穷远点转化为原点,通过研究原点来研究无穷远点的性质,得到系统原点的奇点量和周期常数,中心和等时中心的充分必要条件及其极限环分支. |
| 关键词: 多项式微分系统 无穷远点 中心 等时中心 极限环 |
| DOI： |
| 投稿时间：2010-01-09修订日期：2010-03-19 |
| 基金项目:国家自然科学基金项目(10961011);广西研究生科研创新项目(2009105950701M28)资助。 |
|
| Conditions of Infinity to Be a Center and Isochronous Center and Bifurcation of Limit Cycles for a Differential System |
|
LU Jing-ping
|
| (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, Guangxi, 541004, China) |
| Abstract: |
| The conditions of infinity to be a center and isochronous center and bifurcation of limit cycles for a polynomial differential system are discussed. Infinity can be transferred into the origin by a transformation, and the behavior of system at infinity is investigated by using the methods of the origin. Using the computer algebra system-Mathematica, we compute the singular point values and the period constants at the origin, then give the sufficient and necessary conditions of infinity to be a center, an isochronous center and the bifurcation. |
| Key words: polynomial differential system infinity center isochronous center limit cycle |
