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Dynamical Properties of An Automaton with Memory

  • Michel Cosnard
  • Eric Goles Chacc
Conference paper
  • 171 Downloads
Part of the NATO ASI Series book series (volume 20)

Abstract

Automata networks have been often used to model elementary dynamical properties of neuronal networks (Mc Culloch and Pitts (1943)). Caianiello et al. (1967) generalized the above model in order to introduce the refractory character of the neural response. They proposed to use a memory associated to the system and obtained the following discrete iteration scheme, in order to simulate the response of a single neuron: k-1
$$ {x_{{n + 1}}} = 1\left( {\sum\limits_{{i = 0}}^{{k - 1}} {{a_i}{x_{{n - i}}} - b} } \right) $$
(1)
where xn belongs to (0,1), ai and b are real parameters, k, the size of the memory, a given integer and 1 (u) is 1 if u is non negative and 0 otherwise.

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References

  1. CAIANIELLO E.R. et al., Kybernetik, 4 (1967).Google Scholar
  2. COSNARD M., GOLES E., C. R. Acad. Sc., 299, 10 (1984) pp 459–461.zbMATHMathSciNetGoogle Scholar
  3. GOLES E., Thesis, Grenoble (1985).Google Scholar
  4. MC CULLOCH W., PITTS W., Bull. Math. Biophys., 5 (1943) pp 115–133.CrossRefMathSciNetGoogle Scholar
  5. NAGAMI H. et al., Math. Biosc, 18 (1973)Google Scholar
  6. NAGUMO J., SATO S., Kybernetik, 3 (1972) pp 155–164.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Michel Cosnard
    • 1
  • Eric Goles Chacc
    • 1
  1. 1.CNRS-Laboratoire TIM3/IMA6St Martin d’HèresFrance

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