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.