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 cy...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.展开更多
基金the fund of Youth of Jiangsu University(05JDG011)the National Nature Science Foundation of China(No:90610031)+1 种基金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).
文摘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.
