Chaos control for a single pendulum damping system with proper random phase under forced oscillation (Q539551)

The authors consider the effect of phase of a Gaussian white noise for a single pendulum system with damping. Using Khasminskii's formulation of spherical coordinate and the extension of Wedig's algorithm for linear stochastic systems, they compute the largest Lyapunov exponent. Due to the change of the sign for the largest Lyapunov exponent, the chaotic behaviour of the system is suppressed. In order to confirm the stability of the system, they also analyze the Poincaré surface of the section, the phase portrait and the time evolution.