RESPONSE CHARACTERISTIC OF A MATHEMATICAL NEURON MODEL.

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 having a fixed frequency is applied as an input to the neuron model, 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 function. This result explains the ″unusual and unexpected″ phenomenon found by L. D. Harmon in experimental studies with his transistor neuron model. In addition, a very simple circuit composed of a delay line and a negative resistance element is found to be an analog of our mathematical neuron model.