SYNCHRONIZATION OF INTEGRATE AND FIRE OSCILLATORS WITH GLOBAL COUPLING

We study the behavior of globally coupled assemblies of a large number of integrate and fire oscillators with excitatory pulselike interacti ons. Oo some simple models we show that the additive effects of pulses on the state of integrate and fire oscillators are sufficient for the synchronization of the relaxations of all the oscillators. This synch ronization occurs in two forms depending on the system: either the osc illators evolve ''en bloc'' at the same phase and therefore relax toge ther or the oscillators do not remain in phase but their relaxations o ccur always in stable avalanches. We prove that synchronization can oc cur independently of the convexity or concavity of the oscillator evol ution function. Furthermore the presence of disorder, up to some level , is not only compatible with synchronization, bur removes some possib le degeneracy of identical systems and allows new mechanisms towards t his slate.