The long time behavior of the dynamics of a fast-slow system of ordinary
differential equations is examined. The system is derived from a spatial
discretization of a Korteweg-de Vries-Burgers type equation, with fast
dispersion and slow diffusion. The discretization is based on a model developed
by Goodman and Lax, that is composed of a fast system drifted by a slow forcing
term. A natural split to fast and slow state variables is, however, not
available. Our approach views the limit behavior as an invariant measure of the
fast motion drifted by the slow component, where the known constants of motion
of the fast system are employed as slowly evolving observables; averaging
equations for the latter lead to computation of characteristic features of the
motion. Such computations are presented in the paper.