Cultured in vitro neuronal networks are known to exhibit synchronized bursting events (SBE), during which most of the neurons in the system spike within a time window of approximately 100 msec. Such phenomena can be obtained in model networks based on Markram-Tsodyks frequency-dependent synapses. In order to account correctly for the detailed behavior of SBEs, several modifications have to be implemented in such models. Random input currents have to be introduced to account for the rising profile of SBEs. Dynamic thresholds and inhomogeneity in the distribution of neuronal resistances enable us to describe the profile of activity within the SBE and the heavy-tailed distributions of interspike intervals and interevent intervals. Thus, we can account for the interesting appearance of Lévy distributions in the data.