  We study a modification of the canonical model for networks of class I
neurons, presented by Hoppensteadt and Izhikevich, in which the 'pulse' emitted
by a neuron is smooth rather than a delta-function. We prove two types of
results about synchronization and desynchronization of such networks, the first
type pertaining to 'pulse' functions which are symmetric, and the other type in
the regime in which each neuron is connected to many other neurons.
