Lyapunov exponent and chaos of Duffing's equation perturbed by white noise

摘要

The paper presents a method for computing the top Lyapunov exponents of Duffing's equation perturbed by white noise. It is based on an extension of Wedig's algorithm for linear stochastic systems. The variation of the exponents with damping and harmonic forcing amplitudes is investigated. It is found that for the range of forcing amplitude and damping considered, noise tends to stabilize the system. This effect is more pronounced for the case of varying harmonic forcing amplitude.