We propose a stochastic dynamics for a neural network which accounts for the effects of the refractory periods (absolute and relative) in the dynamics of a single neuron. The dynamics can be solved analytically in an extremely diluted network. We found a very rich scenario that presents retrieval phases and a period doubling route to chaos in the attractors of the overlap order parameter. Our model incorporates some characteristics that make it biologically appealing, such as asymmetric synaptic efficacies, dilution of the synaptic matrix, absolute and relative refractory periods, complex retrieval dynamics, and low levels of activity in the retrieval regime. © 1996 The American Physical Society.

• Received 24 July 1995

DOI:https://doi.org/10.1103/PhysRevE.53.5146