Bifurcations of limit cycles in a perturbed quintic Hamiltonian system with six double homoclinic loops (Q942892)

The paper studies the number and distribution of limit cycles of a quintic planar Hamiltonian system subjected to a seven-degree perturbation. By means of numeric integral computation provided by Mathematica 4.1, at least 45 limit cycles are found 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 presented. The results obtained may be useful in the study of the weakened 16th Hilbert problem.