- Abstract 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 ms. Such phenomena can be obtained in model networks based on Markram–Tsodyks synaptic dynamics. We point out that 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. Introducing inhomogeneity in the distribution of neuronal thresholds and resistances we find that we are able to describe the profile of activity within the SBE and the heavy-tailed distribution of inter-spike interval and inter-event interval. Thus we can account for the interesting appearance of Levy distributions in the data.