Bifurcation set and number of limit cycles in Z2-equivariant planar vector fields of degree 5

An Z2-equivariant polynomial Hamiltonian system of degree 5 with two perturbation terms is considered in this paper. The phase plane (a, b) is divided into 15 different regions which give the bifurcation set of the system. Using the bifurcation theory of planar dynamical system and the method of detection function, we obtain the bifurcation set and the configurations of compound eyes of the system with 21 or 23 limit cycles.