The spontaneous activity of cultured in vitro neuronal networks exhibits rich dynamical behavior. Despite the artiΓΏcial manner of their construction, the networks' activity includes features which seemingly re ect the action of underlying regulating mechanism rather than arbitrary causes and e ects. Here, we study the cultured networks dynamical behavior utilizing a generative modelling approach. The idea is to include the minimal required generic mechanisms to capture the non-autonomous features of the behavior, which can be reproduced by computer modelling, and then, to identify the additional features of biotic regulation in the observed behavior which are beyond the scope of the model. Our model neurons are composed of soma described by the two Morris-Lecar dynamical variables (voltage and fraction of open potassium channels), with dynamical synapses described by the Tsodyks-Markram three variables dynamics. The model neuron satisΓΏes our self-consistency test: when fed with data recorded from a real cultured networks, it exhibits dynamical behavior very close to that of the networks' "representative" neuron. SpeciΓΏcally, it shows similar statistical scaling properties (approximated by similar symmetric LΓ evy distribution with ΓΏnite mean). A network of such M-L elements spontaneously generates (when weak "structured noise" is added) synchronized bursting events (SBEs) similar to the observed ones. Both the neuronal statistical scaling properties within the bursts and the properties of the SBEs time series show generative (a new discussed concept) agreement with the recorded data. Yet, the model network exhibits di erent structure of temporal variations and does not recover the observed hierarchical temporal ordering, unless fed with