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Reduction of Continuous Neuronal Model to Discrete Binary Automata

by Abir Hadriche, Nawel Jmail, Hamadi Ghariani, Abdennaceur Kachouri, Laurent Pezard
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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.

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Index Terms

Computer Science
Information Sciences

Keywords

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

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