Maximal Lyapunov Exponent and Almost-Sure Sample Stability for Coupled Two-Degree-of-Freedom Nonlinear Stochastic Systems
Rong Haiwu, Xu Wei, Fang Tong
(Northwestern Polytechnical University, Xi'an, 710072)

Abstract: In this paper, a perturbation approach is used to calculate the asymptotic growt hrate of stochastically coupled two-degree-of-freedom nonlinear stochastics systems. The noise is assumed to bewhite and of small intensity in order to calculate the explicit asymptotic formulas for the maximum Lyapunov exponent. The a lmost-sure sample stability or instability of the four-dimensional stochastic system depends on the sign of the maximum Lyapunov exponent.
Keyowrds: nonlinear stochastic system, maximum Lyapunov exponent, almost-sure sample stability, stable probability density function, pe rturbation method.