Lyapunov exponents and stochastic stability of quasi-integrable-Hamiltonian systems

The averaged equations of integrable and nonresonant Hamiltonian systems of multi-degree-of-freedom subject to light damping and real noise excitation s of small intensities ave first derived Then, the expression for the large st Lyapunov exponent of the square root of the Hamiltonian is formulated by generalizing the well-known procedure due to Khasminskii to the averaged e quations, from which the stochastic stability and bifurcation phenomena of the original systems can be determined approximately. Linens and nonlinear stochastic systems of two degrees-of-freedom are investigated to illustrate the application of the proposed combination approach of the stochastic ave raging method for quasi-integrable Hamiltonian systems and Khasminskii's pr ocedure.