一类(n+1)次多项式系统极限环的存在性(英文)  

Existence of Limit Cycles for a Class of(n+1)-th Polynomial Systems

作　　者：杜佳[1] 肖箭[1] 查道丽[1] 王瑀[1] 周久红[1] 宋国强[2] 

机构地区：[1]安徽大学数学科学学院,合肥230601 [2]安徽医科大学卫生管理学院,合肥230032

出　　处：《工程数学学报》2014年第2期274-285,共12页Chinese Journal of Engineering Mathematics

基　　金：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 Project of the Postgraduatesfor Anhui University(yfc100020;yfc100028)

摘　　要：本文研究一类(n+1)次多项式系统极限环的存在性及无穷远奇点的类型.根据微分方程几何理论计算焦点量,考虑了系统的中心焦点问题,利用旋转向量场与广义Li′enard系统理论,获得了系统极限环存在的充分条件.同时利用Poincar′e变换,分析了系统无穷远奇点的类型.这些工作突破了已有结论关于系统阶数的局限性,因而具有更广泛的应用范围.In this paper, we investigate the existence of limit cycles and the types of critical points at infinity for a class of （n＋1）-th polynomial systems. According to the geo-metrical theory of differential equation, by computing the focal values, the problem of center and focus is considered. By applying the theories of rotated vector field and generalized Li′enard system, a series of su？cient conditions are developed to guarantee the existence of limit cycles, and the types of critical points at infinity are also discussed by Poincar′e transformation. These works improve the results of the differential system. Therefore, it has wide range of application for accompany systems.

关 键 词：相伴系统 (n+1)次多项式系统 极限环 存在性 无穷远奇点 

分 类 号：O175.12[理学—数学]