一类非多项式平面向量场的极限环(Ⅰ)(英文)  

LIMIT CYCLES FOR A CLASS OF NON-POLYNOMIAL PLANAR VECTOR FIELDS (Ⅰ)

作　　者：杜佳[1] 肖箭[1] 王瑀[1] 周久红[1] 

机构地区：[1]安徽大学数学科学学院,安徽合肥230601

出　　处：《数学杂志》2013年第3期419-431,共13页Journal of Mathematics

基　　金：Supported by the Natural Science Foundation of Anhui Education Committee(KJ2007A003);the"211 Project"for Academic Innovative Teams of Anhui University(KJTD002B);the Doctoral Scientific Research Project for Anhui Medical University(XJ201022);the Key Project for Hefei Normal University(2010kj04zd);the Provincial Excellent Young Talents Foundation for Colleges and Universities of Anhui Province(2011SQRL126);the Academic Innovative Scientific Research Project of Postgraduates for Anhui University(yfc100020;yfc100028)

摘　　要：本文研究了一类非多项式平面向量场的极限环.利用形式级数发,Dulac准则方法,Hopf分支理论,以及广义Li′enard平面向量场理论,获得了判定原点为焦点或者中心,讨论极限环不存在性,解析从原点分支出极限环,以及建立极限环的存在性,唯一性和稳定性等的一些充分条件,推广了文献[5]中的结果.In this article, we study the limit cycles for a class of non-polynomial planar vector fields. By applying Liapunov method theory, the method of Dulac criterion, Hopf bifurcation theory, and the generalized Li@nard planar vector fields theory, we obtain some sufficient conditions for the origin to be a focus or center, for the non-existence of the limit cycles, for analying bifurcating the limit cycles from the origin, and for building the existence, uniqueness and stability of the limit cycles, which generalizes the existing results in [51.

关 键 词：非多项式平面向量场 极限环 形式级数法理论 Dulac准则 Hopf分支理论 广义Li′enard平面向量场 

分 类 号：O175.12[理学—数学]