Complex emergent dynamics in neural networks with synaptic plasticity

This thesis concerns the study of the emerging dynamical regimes in a neural network in the presence of the mechanism of short-term synaptic plasticity. In particular, the aim has been to characterize and to study the collective regimes of synchronization, chaos and criticality. Thanks to the measures developed in the thesis, it has been possible to draw with great precision the phase diagram (hitherto unknown) of the leaky integrate-and-fire single neuron model connected with a Tsodyks-Uziel-Markram model for short-term synaptic plasticity on a mean field and disordered topology, and to elucidate (also analytically, by means of the reduction of the dynamics to a few simple coupled equations) the mechanism by which the model becomes chaotic in the mean field phase, preserves chaos and generates power-law distributed avalanches in the disordered topology.