A discrete map for the dynamics of recurrent excitatory neural networks inthe 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 differen t types of dynamics obtained with simulations of a network of coupled excit atory spike-response neuron models placed under the influence of noise. The n, we derive a discrete map describing the dynamics of large fully connecte d networks. By studying the bifurcation structure of this map, we can deter mine for which ranges of the neuron model parameters the network will displ ay collective oscillations or other types of dynamics. (C) 1998 Elsevier Sc ience Ireland Ltd. All rights reserved.