A discrete map for the dynamics of recurrent excitatory neural networks in the presence of noise

We investigate the effect of the neuron characteristics on the behavior of a recurrent excitatory neural network model. First, we present the different types of dynamics obtained with simulations of a network of coupled excitatory spike-response neuron models placed under the influence of noise. Then, we derive a discrete map describing the dynamics of large fully connected networks. By studying the bifurcation structure of this map, we can determine for which ranges of the neuron model parameters the network will display collective oscillations or other types of dynamics.