摘要
研究一类三次多项式微分系统的中心和焦点的判别及原点为中心时这类系统的相图.首先利用焦点量公式对其进行中心和焦点的判别,然后采用平面奇点分析理论和高阶奇点分析方法对有限处奇点和无穷远奇点的性态进行分析,最后根据积分因子的连续性证明系统(2)在全平面上不存在极限环,并获得上述系统的3个相图.
We discussed the discrimination of center and focus for a class of cubic polynomial differential system and the phase portraits of the system when O（0, 0） was a center. First of all,we used focus quantity formula to distinguish center and forcus,then applyed plane singularity analysis theory and high-order singularity analysis method to analyze the behavior of finite singular points and infinite singular points. Finally , we proved that system（2）had no limit cycle,and gave the global topological phase-portraits of this system.
出处
《湖北大学学报（自然科学版）》
CAS
2015年第2期185-190,共6页
Journal of Hubei University：Natural Science
关键词
奇点
极限环
相图
singularity
limit cycle
phase-portrait
