Bifurcation of limit cycles in a cubic Hamiltonian system with perturbed terms

Bifurcation of limit cycles in a cubic Hamiltonian system with quintic perturbed terms is investigated using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the perturbed cubic Hamiltonian system. The study reveals firstly that there are at most 15 limit cycles in the cubic Hamiltonian system with perturbed terms. The distributed orderliness of the 15 limit cycles is observed and their nicety places are determined. The study also indicates that each of the 15 limit cycles passes the corresponding nicety point. The results presented here are helpful for further investigating the Hilbert's 16th problem.