Suppressing chaos of a complex Duffingʹs system using a random phase

The effect of random phase for a complex Duffingʹs system is investigated. We show as the intensity of random noise properly increases the chaotic dynamical behavior will be suppressed by the criterion of top Lyapunov exponent, which is computed based on the Khasminskiiʹs formulation and the extension of Wedigʹs algorithm for linear stochastic systems. Also Poincaré map analysis, phase plot and the time evolution are carried out to confirm the obtained results of Lyapunov exponent on dynamical behavior including the stability, bifurcation and chaos. Thus excellent agreement between these results is found.