Chaos control of a class of parametrically excited Duffing’s system using a random phase

As the analysis of the chaotic dynamical behavior of a parametric Duffing’s system, we show that chaos can be suppressed by addition the Gauss white noise phase and determined by the sign of the top Lyapunov exponent, which is based on the Khasminskii’s formulation and the extension of Wedig’s algorithm for linear stochastic systems. Also Poincaré map analysis is carried out to confirm the obtained results. So random phase can be realized as one of the methods of chaos control.