Bifurcations of limit cycles in a Z6Z6-equivariant planar vector field of degree 7

In this paper, the weakened Hilbert’s 16th problem for symmetric planar perturbed polynomial Hamiltonian systems is considered. With the help of numerical analysis, by using bifurcation theory of planar dynamical systems and the method of detection function, we show that a Z6Z6-equivariant planar perturbed Hamiltonian vector field of degree 7 has at least 37 limit cycles. The paper also shows the configuration of compound eyes of that Z6Z6-equivariant system.