Phase Effect in Controlling Non-autonomous Chaos in the Presence of Noise

The effect of random phase on the Josephson junction system dynamic model is investigated. It is shown that random phase has the suppressing ability for controlling chaos. The top Lyapunov exponent is used to detect the chaotic dynamics in the system, and the method for calculating the top Lyapunov exponent is based on Khasminskii＇s spherical coordinate formulation for linear stochastic systems. In addition, Poincare map, phase portraits and time evolution are investigated to verify the obtained results. It is found that these results have the excellent agreement.