关于一类非多项式平面微分系统的极限环及分支问题(英文)  

Limit cycle and bifurcation problem for a class of nonpolynomial planar differential systems

作　　者：杜佳[1] 肖箭[1] 张高英[1] 

机构地区：[1]安徽大学数学科学学院,合肥230601

出　　处：《应用数学与计算数学学报》2014年第2期189-199,共11页Communication on Applied Mathematics and Computation

基　　金：Project supported by the Natural Science Foundation of Anhui Education Department(KJ2012A171);the 211 Project of Anhui University(KJTD002B);the Scientific Research of BSKY from Anhui Medical University(XJ201022);the Provincial Excellent Young Talents Foundation for Colleges and Universities of Anhui Province(2011SQRL126);the Academic Innovative Scientific Research Projects of the Postgraduates for Anhui University(yfc100020,yfc100028)

摘　　要：旨在讨论一类非多项式平面微分系统.通过使用Dulac准则和Bendixson准则获得极限环不存在性的充分条件,引入广义Lienard系统理论以研究极限环的存在性及稳定性,应用Hopf分岔理论证明自原点分岔出极限环的充分条件.此外,给出一个范例以验证分析和结果的有效性.This paper aims to discuss a class of the nonpolynomial planar differ- ential systems. The Dulac criterion and the Bendixson criterion are used to obtain some sufficient conditions for the nonexistence of the limit cycle, and the theory of the generalized Lidnard system is introduced to investigate the existence and the stability of the limit cycle. The Hopf bifurcation theory is applied to prove some sufficient conditions for the bifurcating limit cycle from the origin. In addition, one typical example is given to verify the effectiveness of the analyses and results.

关 键 词：非多项式平面微分系统 广义LIÉNARD系统 极限环 Dulac准则 Bendixson准则 Hopf分岔理论 

分 类 号：O175[理学—数学]