CFP last date
22 April 2024
Reseach Article

Reduction of Continuous Neuronal Model to Discrete Binary Automata

by Abir Hadriche, Nawel Jmail, Hamadi Ghariani, Abdennaceur Kachouri, Laurent Pezard
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 69 - Number 24
Year of Publication: 2013
Authors: Abir Hadriche, Nawel Jmail, Hamadi Ghariani, Abdennaceur Kachouri, Laurent Pezard
10.5120/12116-8140

Abir Hadriche, Nawel Jmail, Hamadi Ghariani, Abdennaceur Kachouri, Laurent Pezard . Reduction of Continuous Neuronal Model to Discrete Binary Automata. International Journal of Computer Applications. 69, 24 ( May 2013), 5-10. DOI=10.5120/12116-8140

@article{ 10.5120/12116-8140,
author = { Abir Hadriche, Nawel Jmail, Hamadi Ghariani, Abdennaceur Kachouri, Laurent Pezard },
title = { Reduction of Continuous Neuronal Model to Discrete Binary Automata },
journal = { International Journal of Computer Applications },
issue_date = { May 2013 },
volume = { 69 },
number = { 24 },
month = { May },
year = { 2013 },
issn = { 0975-8887 },
pages = { 5-10 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume69/number24/12116-8140/ },
doi = { 10.5120/12116-8140 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:31:10.276705+05:30
%A Abir Hadriche
%A Nawel Jmail
%A Hamadi Ghariani
%A Abdennaceur Kachouri
%A Laurent Pezard
%T Reduction of Continuous Neuronal Model to Discrete Binary Automata
%J International Journal of Computer Applications
%@ 0975-8887
%V 69
%N 24
%P 5-10
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This article presents the reduction of neuronal models from the classic four-dimensional differential model of Hodgkin and Huxley [7] to discrete binary automata which keep the main properties of more complex models. A reduction of Fitzhugh and Nagumo (FHN) model is performed using a numerical strategy introduced in [3] completed by a linearization in the spirit of McKean model [14]. The resultant discrete binary model keeps the properties of the complete FHN model. The numerical simulations of networks composed by these discrete binary automata demonstrate changes in the system dynamics dependent on the coupling strength. Moreover, for large coupling strength, phase-locking is observed.

References
  1. L. F. Abbott. Modulation of function and gated learning in a network memory. Proceedings of the National Academy of Sciences of USA, 87:9241–9245, 1990.
  2. L. F. Abbott. A network of oscillators. Physica. A, 23:3835–3859, 1990.
  3. L. F. Abbott and Thomas B. Kepler. Model neurons: From Hodgkin-Huxley to Hopfield, 1990.
  4. B. Chopard and M. Droz. Cellular automata modelling of physical systems. ambridge University Press, Cambridge UK, 1998.
  5. M. Denman-Johnson and S. Coombes. Continuum of weakly coupled oscillatory mckean neurons. Physica Review E, 67, May 2003.
  6. R. Fitzhugh and E. M. Izhikevich. Fitzhugh-Nagumo model. Scholarpedia, 1:1349, 2006.
  7. A. L Hodgkin and Huxley. A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. Physical, 117:500–544, 1952.
  8. J. J. Hopfield. Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America, 79(8):2554–2558, 1982.
  9. E. M. Izhikevich. Hybrid spiking models. Philosophical Transactions of the Royal Society A, 368:5061–5070, 2010.
  10. Eugene M. Izhikevich, A. Gally. Jeo, and M. Edelman Gerald. Spike-timing dynamics of neuronal groups. Cerebral cortex, 14:933–944, 2004.
  11. Winfried Just, Sungwoo Ahn, and David Terman. Minimal attractors in digraph system models of neuronal networks. Physica D, 237:3186–3196, 2008.
  12. T. B. Kepler, L. F. Abbott, and E. Marder. Reduction of conductance-based neuron models. Biological Cybernetics, 66:381–387, 1992.
  13. V. I. Krinskii and Y. M. Kokoz. Analysis of equations of excitable memebranes. I. Reduction of the Hodgkin- Huxley equations to a second order system. Biofizika, 18:506–511, 1973.
  14. H P. McKean. Nagumo's Equation. Advances in Mathematics, 4:209–223, 1970.
  15. D. Terman, S. Ahn, X. Wang, and W. Just. Reducing neuronal networks to discrete dynamics. Physica D, 237:324–338, 2008.
Index Terms

Computer Science
Information Sciences

Keywords

neuronal models Hodgkin and Huxley model FitzHugh Nagumo model binary model time discrete reduction