Analysis on bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system

Research on the bifurcations of the multiple limit cycles for a parametrically and externally excited mechanical system is presented in this paper. The original mechanical system is first transformed to the averaged equation in the Cartesian form, which is in the form of a Z2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, using the bifurcation theory of planar dynamical system and the method of detection function, the bifurcations of the multiple limit cycles of the system are investigated and the configurations of compound eyes are also obtained.