Bifurcations of a generalized van der Pol oscillator with strong nonlinearity

A generalized van der Pol oscillator with parametric excitation is studied for its bifurcation. On the basis of the MLP method, we enable a strongly nonlinear system to be transformed into a small parameter system. The bifurcation response equation of a 1/2 subharmonic resonance system is determined by the multiple scales method. According to the singularity theory, the bifurcation of equilibrium points is analyzed. The stability of the zero solution is researched by the eigenvalues of the variational matrix and the bifurcation sets are constructed in various regions of the parameter plane.