Abstract
AbstractA neuron can be considered as a threshold element with refractory period. In order to arrive at a generalized treatment of several neuron models proposed in the past, this paper considers a certain type of threshold element network model which has, in addition to exponential decay of refractoriness with time, the effect of past excitations included in the exponent. The periodic behavior of such a network is analyzed and the existence condition for arbitrarily assumed periodic sequence and its generation rule are derived. The procedure is closely related to the continued fraction expansion of a rational number and the sequence is uniquely determined from the network dynamics. The entire set of periodic sequences produced by a network can be derived by the proposed procedure. Lastly, the relation between the proposed network model and the analog neuron model is discussed.
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