We propose a stochastic dynamics for a neural network which accounts for the effects of the refractory periods ͑absolute and relative͒ 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

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... efficacies, dilution of the synaptic matrix, absolute and relative refractory periods, complex retrieval dynamics, and low levels of activity in the retrieval regime.