Analysis of a Parametrically Driven Pendulum
  We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also conduct a symbolic analysis of the model, which demonstrates that the symbolic dynamics of two-dimensional maps can be applied effectively to the study of ordinary differential equations in order to gain global knowledge about them. 
Randy Kobes, Junxian Liu, Slaven Peles