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We analyze the physical mechanisms leading either to synchronization or tothe formation of spatio-temporal patterns in a lattice model of pulse-coupledoscillators. In order to make the system tractable from a mathematical point ofview we study a one-dimensional ring with unidirectional coupling. In such asituation, exact results concerning the stability of the fixed of the dynamicevolution of the lattice can be obtained. Furthermore, we show that thisstability is the responsible for the different behaviors.Comment: 8 pages, 2 ps figures, epsf.sty, RevTeX. To appear in Phys. Rev.

Mechanisms of synchronization and pattern formation in a lattice of pulse-coupled oscillators