Abstract
A mathematical neuron model defined by a difference equation was investigated when it was exposed to an environment of a periodic input stimulus. It is shown that pulse sequences constructed in advance by a particular method are actually realizable as the output of the system and the condition for the output sequence is also obtained with respect to the magnitude of the input. The results are interesting from a point of view of number theory.
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References
Nagumo, J., Sato, S.: On a response characteristics of a mathematical neuron model, Kybernetik 10, 155–164 (1972)
Sato, S.: Mathematical properties of responses of a neuron model, A system as a rational number generator, Kybernetik 11, 208–216 (1972)
Nagumo, J.: On a function which is defined by solutions of a nonlinear difference equation, non-autonomous system, Paper of Technical Group on Non-linear Problem, The Institute of Electronics and Communication Engineers of Japan, NLP 72-10 (1972) (in Japanese)
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Sato, S., Hatta, M. & Nagumo, JI. Response characteristics of a neuron model to a periodic input. Kybernetik 16, 1–8 (1974). https://doi.org/10.1007/BF00270290
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DOI: https://doi.org/10.1007/BF00270290