Catastrophe control of a nonlinear oscillator under parametric excitations

The example of the roll motion of a biased ship in longitudinal waves is taken to determine the vibration solutions to the nonlinear oscillator by applying catastrophe and bifurcation theory in this paper. First, the catastrophe characteristic of the roll motion of a biased ship in longitudinal waves is proved by transforming the governing equation of the motion to butterfly catastrophe model. Then, the critical point of catastrophe occurrence is found by applying multiple time scale perturbation method and bifurcation analysis to the governing equation. Last, controller is designed to control the critical point in a stable area, which restricted the catastrophe phenomenon of the roll motion by simulation verification.