MAXIMAL LYAPUNOV EXPONENT AND ALMOST-SURE STABILITY FOR COUPLED 2-DEGREE-OF-FREEDOM STOCHASTIC-SYSTEMS

In this paper, a perturbation approach is used to calculate the asympt otic growth rate of stochastically coupled two-degree-of-freedom syste ms. The noise is assumed to be white and of small intensity in order t o calculate the explicit asymptotic formulas for the maximum Lyapunov exponent. The Lyapunov exponents and rotation number for each degree-o f-freedom are obtained in the Appendix. The almost-sure stability or i nstability of the four-dimensional stochastic system depends on the si gn of the maximum Lyapunov exponent. The results presented here match those presented by the first author and others using the method of sto chastic averaging, where approximate Ito equations in amplitudes and p hase are obtained in the sense of weak convergence.