Moment Lyapunov exponents and stochastic stability for two coupled oscillators

Abstract

The Lyapunov exponent and moment Lyapunov exponent of two degree-of-freedom linear systems subjected to white noise parametric excitation are investigated.Through a perturbation method we obtain the explicit asymptotic expressions for these exponents in the presence of low intensity noise.The Lyapunov exponent and moment Lyapunov exponents are important characteristics for determining the almostsure and moment stability of a stochastic dynamical system.As an example, we study the almost-sure and moment stability of the flexural-torsion stability of a thin elastic beam subjected to a stochastically fluctuating follower force.The validity of the approximate results for moment Lyapunov exponents is checked by a numerical Monte Carlo simulation for these stochastic systems.