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

摘要

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 in the Hamiltonian system under the perturbed term of degree 5. Additionally, various distributions of limit cycles are given by numerical exploration.