APPLICATION OF THE SLAVING PRINCIPLE TO NONLINEAR NON-MARKOVIAN SYSTEMS

We study a set of nonlinear stochastic equations that describe a large class of nonlinear multidimensional non-Markovian dynamical systems d riven by Ornstein-Uhlenbeck (OU) noises, and a class of nonlinear mult idimensional differential stochastic equations driven by dichotomous n oises. By use of the stochastic generalization of the usual adiabatic approximation, the equations for the order parameters are obtained. Th e statistical properties of the new stochastic variables are studied. In the circumstances of OU noises or dichotomous noises, we derive the approximate Fokker-Planck equations (AFPE's) corresponding to the equ ations for the order parameters and calculate the stationary solutions of AFPE's.