Z_2-Equivariant Cubic System Which Yields 13 Limit Cycles

作     者：Yi-rong LIU Ji-bin LI 

作者机构：School of MathematicsCentral South University Department of MathematicsZhejiang Normal University School of ScienceKunming University of Science and Technology 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2014年第30卷第3期

页      面：781-800页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.11371373 and 10831003) 

主　　题：planar dynamical system limit cycles bifurcations Lyapnov constant weak focus 

摘      要：For the planar Z2-equivariant cubic systems having two elementary focuses, the characterization of a bi-center problem and shortened expressions of the first six Lyapunov constants are completely solved. The necessary and sufficient conditions for the existence of the bi-center are obtained. On the basis of this work, in this paper, we show that under small Z2-equivariant cubic perturbations, this cubic system has at least 13 limit cycles with the scheme 1 6 ∪ 6.