Thirteen limit cycles for a class of cubic Hamiltonian system with higher-order perturbed terms

The number and distribution of limit cycles of a cubic Hamiltonian system under higher-order perturbed terms is investigated. By using the bifurcation theory and the method of detection function, we obtain that there exist at least 13 limit cycles with the distribution C71⊃2[C32⊃2C12] in the Hamiltonian system under the perturbed term of degree 5. Additionally, various distributions of limit cycles are given by numerical exploration.