Applications of the Stochastic Adiabatic Approximation

In the previous paperi^[1], we have studied a class of nonlinear stochastic dynamical systems using the stochastic adiabatic approximation. A closed evolution equation for the slow variable u^t is obtained. In the present study, we use the methods proposed by the authors in Refs. [2] and [3] to treat the closed u^t equation which is derived by means of the new eliminating technique developed in Ref. [1] recently. Two important stochastic dynamical models, the simplified single-mode laser model and the stochastic Haken model, are treated concretely. The coupling effect of the additive and the multiplicative noise is found.