- Stereotypic paroxysmal discharges that propagate in neocortical tissues after electrical stimulations are used as a probe for studying cortical circuitry. I use modeling to investigate the effects of sparse connectivity, heterogeneity of intrinsic neuronal properties, and synaptic noise on synchronization of evoked propagating neuronal discharges in a network of excitatory, regular spiking neurons with spatially decaying connectivity. The global coherence of the traveling discharge is characterized by the correlation function between spike trains of neurons, averaged over all the pairs of neurons in the system at the same distance. Local coherence of two neurons is characterized by their correlation function averaged over many trials or, for persistent activity, over a long time interval. Spike synchronization between neurons emerges as a result of the transient activity; if activity is persistent, there is no synchrony, and cross-correlation functions are flat. During discharge propagation, system-average cross-correlation between neurons does not depend on their mutual distance except for a time shift. Spike synchronization occurs only when the average number of synapses M a cell receives is large enough. As M increases, there is a cross-over from an asynchronized to a synchronized discharge. Synaptic depression appears to help synchrony; it reduces the M value at the cross-over. The strengths of alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-D-aspartate (NMDA) conductances affect synchrony only weakly. Spike synchronization is robust even with large levels of heterogeneity. Synaptic noise reduces synchrony, but strong synchrony is observed at a noise level that cannot evoke spontaneous discharges. System-average spike synchronization is determined by the levels of sparseness, heterogeneity, and noise, whereas trial-average spike synchronization is determined only by the noise level. Therefore, I predict that experiments will reveal local, two-cell spike synchrony, but not global synchrony.