An analysis of a neural network with a fixed memory span

A study is made of a discrete neural model with a fixed memory span h. The model is described by a system of coupled nonlinear delay differential equations of the Krasovskii-Razumikhin type. After establishing some of the general properties of the model the effects of the memory spans are discussed in the cellular and network levels. The results of some simulations are presented, showing a good agreement with theory. Activity profiles in both models agree for large h. For increasing h the neutral model with fixed memory span approaches the neural model with cumulative memory. However, the agreement between activity profiles of both models is lost for small memory spans h. For small h, the adaptation property of neurons to external inputs, and the causal property of the model disappear