Stochastic stability of quasi-integrable-Hamiltonian systems with Gaussian white noise excitations

The averaged equations of nonresonant integrable Hamiltonian systems of multi-degree-of-freedom subject to light damping and weakly Gaussian white noise excitations are first derived by using the stochastic averaging method for quasi-integrable Hamiltonian systems. Then, the expression for the largest Lyapunov exponent of the square root of the Hamiltonian is given by generalizing the well-known procedure due to Khasminskii to the averaged equations, from which the stochastic stability and bifurcation phenomena of the original systems dan be determined approximately. A nonlinear stochastic system of two-degree-of-freedom is investigated to illustrate the application of the proposed approach.