MEAN-FIELD EQUATIONS, BIFURCATION MAP AND ROUTE TO CHAOS IN DISCRETE-TIME NEURAL NETWORKS

We investigate the dynamical behaviour of neural networks with asymmetric synaptic weights, in the presence of random thresholds. We inspect low gain dynamics before using mean-field equations to study the bifurcations of the fixed points and the change of regime that occurs when varying control parameters. We infer different areas with various regimes summarized by a bifurcation map in the parameter space. We numerically show the occurence of chaos that arises generically by a quasi-periodicity route. We then discuss some features of our system in relation with biological observations such as low firing rates and refractory periods.