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Abstract
Recently, Nagumo and Sato proposed a mathematical neuron model in the form of a nonlinear difference equation and investigated its response characteristic. The result showed that the input-output relationship of the neuron model is quite complicated and takes the form of an extended Cantor's function. It also explained the “unusual and unsuspected” phenomenon found by Harmon in experimental studies with his transistor neuron model. — In this paper, a fraction representation of a sequence of pulses is proposed. A mathematical treatment of the same neuron model based on the representation gives the same result as in the previous paper. Moreover, many mathematical properties, including the one where the ratio of the number of 1's contained in a cycle of a sequence to the length of the cycle gives any rational number between 0 and 1, were obtained by investigating sequences generated by the model.
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