The number and distributions of limit cycles for a class of cubic near-Hamiltonian systems

This paper concerns with the number of limit cycles for a cubic Hamiltonian system under cubic perturbation. The fact that there exist 9–11 limit cycles is proved. The different distributions of limit cycles are given by using methods of bifurcation theory and qualitative analysis, among which two distributions of eleven limit cycles are new.  2005 Elsevier Inc. All rights reserved