Chaos control of Duffing systems by random phase

In this paper, the effect of random phase for Duffing systems is investigated. We show that random phase can generate chaos or suppress chaos by the average of top Lyapunov exponent, which is computed based on Khasminskii's spherical coordinate formulation for linear stochastic systems. In addition, phase portraits, Poincaré surface of section and time evolution are studied to confirm the obtained results. Both methods lead to fully consistent results.