  We prove that a topologically generic network (an open and dense set of
networks) of three or more inhibitory neurons have periodic behavior with a
finite number of limit cycles that persist under small perturbations of the
structure of the network. The network is modeled by the Poincare transformation
which is piecewise continuous and locally contractive on a compact region B of
a finite dimensional manifold, with the separation property: it transforms
homeomorphically the different continuity pieces of B into pairwise disjoint
sets.
