Bifurcation solutions of resonant cases of nonlinear Mathieu equations (Q1176069)

The nonlinear Mathieu equation is investigated close to resonance. Using Lyapunov-Schmidt reduction the bifurcation solutions including the main resonance, subharmonic, superharmonic and fractal resonance are studied. A stratification of the parameter space into six regions of topologically equivalent response diagrams is given. This analysis covers many interesting models, among them the Mathieu van der Pol equation, the Mathieu-Duffing equation and the pendulum with vertically vibrating support.