Bifurcations of limit cycles for a perturbed quintic Hamiltonian system with four infinite singular points

By using the theory of bifurcations of dynamical systems and the method of detection function to investigate the bifurcation of limit cycles of a perturbed quintic Hamiltonian system with 25 finite singular points and four infinite singular points. From the detection functions for the perturbed system, we prove that under different determined parameter condition, the given system has at least 22 and 20 limit cycles and the configurations of compound eyes are also obtained.