  We investigate the ground state of a system of interacting particles in small
nonlinear lattices with M > 2 sites, using as a prototypical example the
discrete nonlinear Schroedinger equation that has been recently used
extensively in the contexts of nonlinear optics of waveguide arrays, and
Bose-Einstein condensates in optical lattices. We find that, in the presence of
attractive interactions, the dynamical scenario relevant to the ground state
and the lowest-energy modes of such few-site nonlinear lattices reveals a
variety of nontrivial features that are absent in the large/infinite lattice
limits: the single-pulse solution and the uniform solution are found to coexist
in a finite range of the lattice intersite coupling where, depending on the
latter, one of them represents the ground state; in addition, the single-pulse
mode does not even exist beyond a critical parametric threshold. Finally, the
onset of the ground state (modulational) instability appears to be intimately
connected with a non-standard (``double transcritical'') type of bifurcation
that, to the best of our knowledge, has not been reported previously in other
physical systems.
