Bifurcations of Limit Cycles from Asymmetric Hamiltonian Systems with Five-Order Perturbed Terms

The bifurcation of limit cycles is investigated from asymmetric cubic Hamiltonian systems under the perturbation of five-order polynomials. The approach applies Green’s theorem to the method of detection function: First, the Abelian integrals with irregular regions are computed, improving the accuracy of bifurcation parameter values. Second, it is shown that there exist at least 11 limit cycles with two distinct distributions. Third, precise detection curves are presented to validate all analytical results. Finally, four cases are investigated for the number and distribution of limit cycles by considering Hopf, heteroclinic, and homoclinic bifurcation values to obtain parameter conditions.