Bifurcations of Limit Cycles in A Perturbed Quintic Hamiltonian System with Six Double Homoclinic Loops  

作　　者：Yong-xi Gao Yu-hai Wu Li-xin Tian 

机构地区：[1]Department of Mathematics, Jiang Su University, Zhenjiang 212013, China

出　　处：《Acta Mathematicae Applicatae Sinica》2008年第2期313-328,共16页应用数学学报（英文版）

基　　金：the fund of Youth of Jiangsu University(05JDG011);the National Nature Science Foundation of China(No:90610031);Outstanding Personnel Program in Six Fields of Jiangsu(No:6-A-029);Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of POE,China(No:2002-383).

摘　　要：This paper concerns with the number and distributions of limit cycles of a quintic subject to a seven-degree perturbation. With the aid of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found in the above system by applying the method of double homoclinic loops bifurcation, Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are also shown. The results obtained are useful to the study of the weakened 16th Hilbert Problem.This paper concerns with the number and distributions of limit cycles of a quintic subject to a seven-degree perturbation. With the aid of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found in the above system by applying the method of double homoclinic loops bifurcation, Hopf bifurcation and qualitative analysis. The four configurations of 45 limit cycles of the system are also shown. The results obtained are useful to the study of the weakened 16th Hilbert Problem.

关 键 词：limit cycles the Hilbert＇s 16th problem the double homoclinic loops stability Poincare-Bendixsontheorem 

分 类 号：O211.4[理学—概率论与数理统计]