, Volume 10, Issue 1, pp 38–44 | Cite as

A method of analysis of the models of neural nets

  • E. Burattini
  • V. Liesis


Taking into account Caianiello's work of 1961 a model of a neuron quite similar to his is proposed and studied. For this model, where a temporal summation and a period of refractoriness are assumed, a mathematical approach and a simulation on computer were realized. Particular types of nets were used, namely: nets with topological structures, and fully random nets. The difference between the two types is that the first type has a two-dimensional square structure and depends on the rules of the formation of connection between the neurons, while the second type is realized by means of the probability distribution function governing the formation of the structure of the net.

These types of neural nets are analysed by means of a method which permits to obtain various parameters which characterize their behaviour in time and space in terms of the trajectory of the system. Many experiments are also reported; the statistical analyses, made on them, show the great importance and influence of refractoriness on the behaviour of neural networks.

In the last part of the work an interesting case is reported, in which the reaction of the net to a disturbance shows that a kind of adaptation takes place, although the structure of the net stays unchanged.


Neural Network Distribution Function Probability Distribution Interesting Case Probability Distribution Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Caianiello, E. R.: Outline of a theory of thought-processes and thinking machines. J. theor. Biol. 1, 204–235 (1961).Google Scholar
  2. 2.
    — Luca, A., de, Ricciardi, L. M.: Reverberations and control of neural networks. Kybernetik 4, 10–18 (1967).Google Scholar
  3. 3.
    Aiello, A., Burattini, E., Caianiello, E. R.: Synthesis of reverberating neural networks. Kybernetik 7, 191–195 (1970).Google Scholar
  4. 4.
    Beurle, R. L.: Properties of a mass of cells capable of regenerating pulses. Phil. Trans. B 669, No. 3240, 55 (1956).Google Scholar
  5. 5.
    Ishihara, T.: On Caianiello's neuronic equations. Math. Japonicae 15, (1970).Google Scholar
  6. 6.
    - Local reverberations in the nervous system and memory (Preprint).Google Scholar
  7. 7.
    Liesis, V. I., Zukauskas, K. P.: The simulation of a neural net (1. The properties of a net composed of neuron-like elements). Proc. Acad. Sci. Lithuanian SSR, Ser. B, 4 (43) 165–172 (1965) [in Russian].Google Scholar
  8. 8.
    Zukauskas, K. P., Liesis, V. I.: The construction of a model of neural nets from threshold elements without inhibitory inputs [in Russian], In: The dynamics of neural nets, p. 42–49. Vilnius 1966.Google Scholar
  9. 9.
    Liesis, V. I.: The simulation of the random neural nets by digital computers [in Russian]. In: The problems of bionics, p. 204–210. Moscow 1967.Google Scholar
  10. 10.
    -Zukauskas, K. P.: The statistical investigations of the models of neural nets [in Russian]. Proc. of the I Symposium on Statistical Problems in Technical Cybernetics, pt. II, Moscow 1967, p. 61–62.Google Scholar
  11. 11.
    - -The trajectories of the model of neural net in the phase-space [in Russian]. Proc. of the Symposium on applied mathematics and Cybernetics, Gorkij 1967, p. 194.Google Scholar
  12. 12.
    -Investigation of the activity and possibilities of information processing in the models of random neural nets. Doctoral dissertation, Vilnius, 1970 [in Russian].Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • E. Burattini
    • 1
  • V. Liesis
    • 1
  1. 1.Laboratorio di Cibernetica del C.N.R.Arco Felice, NaplesItaly

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