RAPID PHASE-LOCKING IN SYSTEMS OF PULSE-COUPLED OSCILLATORS WITH DELAYS

The dynamical evolution of a system of integrate-and-fire units with d elayed excitatory coupling is analyzed. The connectivity is arbitrary except for a normalization of the total input to each unit. It is show n that the system converges to a periodic solution where all units are phase locked but do not necessarily fire in unison. In the case of di screte and uniform delays, a periodic solution is reached after a fini te time. For a delay distribution with finite support, an attractor is , in general, only reached asymptotically.