Moment Lyapunov Exponent and Stochastic Stability of Two Coupled Oscillators Driven by Real Noise

Abstract

In a recent paper an asymptotic approximation for the moment Lyapunov exponent, g(p), of two coupled oscillators driven by a small intensity real noise was obtained. The utility of that result is limited by the fact that it was obtained under the assumption that the moment p is small, a limitation which precludes, for example, the determination of the stability index. In this paper that limitation is removed and an asymptotic approximation valid for arbitrary p is obtained. The results are applied to study the moment stability of the stationary solutions of structural and mechanical systems subjected to stochastic excitation.