We present long-term (approximately hours) measurements of the spontaneous activity of two-dimensional cortical cell neural networks placed on multielectrode arrays. We compare histograms of single neuron interspike intervals and the network intersynchronized bursting events intervals. In addition, the effect of Ca concentration on the network activity is being studied. At 1 mM Ca concentration, the network exhibits periodic synchronized bursting that fades away after about 20 min. We present a feedback-regulated integrate and fire model to account for the observations. In the model we include two additional features: dynamical threshold and synapse fatigue.