一类五次微分系统的定性分析  

On Qualitative Analysis for a Class of Fifth Differential Systems

作　　者：卢景苹[1] 黄文韬[2] 

机构地区：[1]广西民族师范学院数学与计算机科学系,广西崇左532200 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《数学的实践与认识》2013年第4期225-231,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10961011);广西教育厅高校科研项目(201204LX482)

摘　　要：对一类五次平面多项式微分系统进行了定性分析.给出原点的中心与等时中心条件及极限环的存在性.研究了此系统无穷远点的性态,该无穷远点是高次奇点,并运用把大角域分为若干小角域的方法对此高次奇点在不定号情形下轨线的分布情况进行讨论.In this paper, the qualitative nature for a class of fifth planax polynomial differential system is investigated. The conditions of center and isochronous center and the existence of limit cycles are given. At the same time, the properties of system at infinity which is a higher order singular point is investigated, and the distribution of trajectories of higher order .singular point in the case of undetermined signs is discussed by the method of dividing bighorn domain into several small-angle domain.

关 键 词：极限环 无穷远点 中心 等时中心 高次奇点 

分 类 号：O175.12[理学—数学]