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Abstract
A mathematical neuron model in the form of a nonlinear difference equation is proposed and its response characteristic is investigated. If a sequence of pulses with a fixed frequency is applied to the neuron model as an input, and the amplitude of the input pulses is progressively decreased, the firing frequency of the neuron model, regarded as the output, also decreases. The relationship between them is quite complicated, but a mathematical investigation reveals that it takes the form of an extended Cantor's function. This result explains the “unusual and unsuspected” phenomenon which was found by L. D. Harmon in experimental studies with his transistor neuron models. Besides this, as an analogue of our mathematical neuron model, a very simple circuit composed of a delay line and a negative resistance element is presented and discussed.
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