Neuron synchronization is thought to play major functional roles in the brain. To gain understanding of synchronization mechanisms, we used in vitro large-scale networks of cortical neurons who are known to synchronize spontaneously. We first showed that the time series of synchronization events display complex statistics that current models fall short of explaining. Using numerical simulations, we demonstrated that the incorporation of three adaptive processes (short-term synaptic facilitation, fast fatigue and slow fatigue) is sufficient to reconstruct the experimentally-observed complex statistics. Furthermore, by systematically varying the recurrent excitation in the model, we have shown that experimental cultures appear to operate in an intermediate weakly-synchronized regime in which synchronous events are neither regular nor Poisson. Taken together, the results demonstrate that event-time-series statistics are informative about underlying neural mechanisms and their working points. We feel that these statistics tend to be overlooked by the majority of scientists, who focus more on event magnitudes.