  In this paper we examine the spatio-temporal dynamics of two nonlinearly
coupled wave triplets sharing two common modes. Our basic findings are the
following. When spatial dependence is absent, the homogeneous manifold so
obtained can be chaotic or regular. If chaotic, it drives energy diffusion from
long to small wavelengths as soon as inhomogeneous perturbations are added to
the system. If regular, one may yet have two distinct cases: (i) energy
diffusion is again present if the inhomogeneous modes are linearly unstable and
triplets are effectively coupled; (ii) energy diffusion is absent if the
inhomogeneous modes are linearly stable or the triplets are uncoupled.

Chaotic Dynamics;Chaotic Dynamics