One dimensional approximation for a class of second order stochastic oscillators with strong coupling is studied. First random dynamics of the linear system is shown to be one dimensional Wiener process. Then by some direct estimates on solutions and random invariant manifold reduction, the random dynamics of the second order stochastic nonlinear oscillators is shown to be described by one dimensional system.

second order stochastic oscillators, strong coupling, random dynamical systems, random invariant manifold.