Detection function method and its application to a class of quintic Hamiltonian systems with quintic perturbations

By using the bifurcation theory of planar dynamical systems and the method of detection functions to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system. It is shown that under two different sets of controlled parameters, the given system has at least 23 limit cycles having two different configurations of the compound eyes, respectively.