一类四次微分自治系统原点的中心条件和极限环  

Center conditions and limit cycles for a quartic differential autonomous system

作　　者：黄文武[1] 范兴宇[2] 

机构地区：[1]桂林电子科技大学职业技术学院,广西北海536000 [2]桂林电子科技大学商学院,广西桂林541004

出　　处：《南阳师范学院学报》2012年第9期5-7,共3页Journal of Nanyang Normal University

基　　金：国家自然科学基金项目(10961011);广西自然科学基金项目(2011GXNSFA018134)

摘　　要：讨论一类四次多项式微分系统的中心条件与极限环分支问题.通过对该系统所对应的伴随复系统奇点量的计算及证明,得到系统的原点为中心的充要条件.从奇点量导出焦点量,得到了原点成为6阶细焦点的条件,证明了该系统可从原点领域分支出5个小振幅极限环.In this paper, the bifurcation of limit cycles and conditions of origin to be a center for a quartic polynomial system is investigated. By the computation of the singular point values for the concomitant complex system of the real system, and prove strictly the suffciency for the conditions, we obtain the necessary conditions of origin of system to be a center. The focal values are derived from of the singular points, and the conditions is obtained that the origin to be a 6 order weak focal. Finally, 5 small amplitude limit cycles in the neighborhood of the origin in this system is proved.

关 键 词：四次系统 奇点量 焦点量 极限环 

分 类 号：O172.1[理学—数学]