Bifurcations of Multiple Limit Cycles for a Parametrically and Externally Excited Mechanical System

In order to conduct research on the bifurcations of multiple limit cycles for a parametrically and externally excited mechanical system, the vector field of the averaged equations in the form of a perturbed polynomial Hamiltonian system of degree 7 through perturbed analysis was established. By using the bifurcation theory of planar dynamical system and the Maple symbolic computation program, we controlled the parameters to obtain 40 limit cycles under one group of control conditions and the configurations of compound eyes were also obtained. This result may serve as theoretical reference for the control problem of a parametrically and externally excited mechanical system.