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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Caianiello, E. R.: Outline of a theory of thought-processes and thinking machines. J. theor. Biol. 1, 204–235 (1961).
Caianiello, E. R., DeLuca, A.: Decision equation for binary systems. Application to neuronal behavior. Kybernetik 3, 33–40 (1966).
Hardy, G. H., Wright, E. M.: An introduction to the theory of numbers, p. 54. Oxford: Clarendon Press 1960.
Harmon, L. D.: Studies with artificial neurons, I: Properties and functions of an artificial neuron. Kybernetik 1, 89–101 (1961).
Nagumo, J., Shimura, M.: Self-oscillation in a transmission line with a tunnel diode. Proc. Inst. Radio Engineers 49, 1281–1291 (1961).
Titchmarsh, E. C.: The theory of functions, p. 366. Oxford: Clarendon Press 1968.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Nagumo, J., Sato, S. On a response characteristic of a mathematical neuron model. Kybernetik 10, 155–164 (1972). https://doi.org/10.1007/BF00290514
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00290514