Dynamics of a random neural network with synaptic depression

We consider a randomly connected neural network with linear threshold elements which update in discrete time steps. The two main features of the network are: (1) equally distributed and purely excitatory connections and (2) synaptic depression after repetitive firing. We focus on the time evolution of the expected network activity. The four types of qualitative behavior are investigated: singular excitation, convergence to a constant activity, oscillation, and chaos. Their occurrence is discussed as a function of the average number of connections and the synaptic depression time. Our model relies on experiments with a slice culture of disinhibited embryonic rat spinal cord. The dynamics of these networks essentially depends on the following characteristics: the low non-structured connectivity, the high synaptic depression time and the large EPSP with respect to the threshold value