  We analyze the physical mechanisms leading either to synchronization or to
the formation of spatio-temporal patterns in a lattice model of pulse-coupled
oscillators. In order to make the system tractable from a mathematical point of
view we study a one-dimensional ring with unidirectional coupling. In such a
situation, exact results concerning the stability of the fixed of the dynamic
evolution of the lattice can be obtained. Furthermore, we show that this
stability is the responsible for the different behaviors.
