Abstract
This paper deals with the effect of phase of a Gaussian white noise for a single pendulum system with damping. Based on the Khasminskii’s formulation of spherical coordinate and the extension of Wedig’s algorithm for linear stochastic system, the largest Lyapunov exponent is computed. Due to the change of the sign for the largest Lyapunov exponent, the chaotic behavior of the system is suppressed. Also Poincare surface of section, phase portrait and the time evolution are analyzed to confirm the stability of the system, which demonstrates the above control methods are effective.
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