  We analyze the dynamics of a deterministic model of inhibitory neuronal
networks proving that the discontinuities of the Poincare map produce a never
empty chaotic set, while its continuity pieces produce stable orbits. We
classify the systems in three types: the almost everywhere (a.e.) chaotic, the
a.e. stable, and the combined systems. The a.e. stable are periodic and chaos
appears as bifurcations. We prove that a.e. stable systems exhibit limit
cycles, attracting a.e. the orbits.
