Bifurcations of Limit Cycles in a Z_4-Equivariant Quintic Planar Vector Field

作     者：Yu Hai WU Xue Di WANG Li Xin TIAN 

作者机构：Department of Mathematics Jiangsu University Zhenjiang 212013 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2010年第26卷第4期

页      面：779-798页

核心收录：

学科分类：1305[艺术学-设计学（可授艺术学、工学学位）] 13[艺术学] 07[理学] 08[工学] 080203[工学-机械设计及理论] 070104[理学-应用数学] 081304[工学-建筑技术科学] 0802[工学-机械工程] 0813[工学-建筑学] 0701[理学-数学] 080201[工学-机械制造及其自动化] 

基　　金：Supported by Fund of Youth of Jiangsu University (Grant No. 05JDG011) National Natural Science Foundation of China (Grant No. 10771088) 

主　　题：compounded cycle double homoclinic loops stability bifurcation limit cycles distribution of limit cycles 

摘      要：In this paper, a Z4-equivariant quintic planar vector field is studied. The Hopf bifurcation method and polycycle bifurcation method are combined to study the limit cycles bifurcated from the compounded cycle with 4 hyperbolic saddle points. It is found that this special quintic planar polynomial system has at least four large limit cycles which surround all singular points. By applying the double homoclinic loops bifurcation method and Hopf bifurcation method, we conclude that 28 limit cycles with two different configurations exist in this special planar polynomial system. The results acquired in this paper are useful for studying the weakened 16th Hilbert＇s Problem.