STOCHASTIC STABILITY OF TWO COUPLED OSCILLATORS IN RESONANCE

摘要

We obtain an approximation for the moment Lyapunov exponent of two coupled oscillators with commensurable frequencies driven by a small intensity real noise. A stochastic averaging scheme along with a Girsanov transformation and the Feynman-Kac formula are used to explicitly obtain the eigenvalue problem for the moment Lyapunov exponent. An orthogonal expansion for the eigenvalue problem based on Galerkin method is used to derive the stability results.