[Une méthode analytique pour le calcul des courbes bifurcation de Hopf dans les champs neuronaux avec retards dépendant de lʼespace]
Dans ce compte-rendu, on donne une paramètrisation des courbes de valeurs propres imaginaires pures, dans le plan des paramètres décrivant le terme des retards, pour les équation linéarisées des champs neuronaux avec retards dépendant de lʼespace. Afin de savoir si la valeur propre de plus grande partie réelle, est imaginaire pure, on doit calculer un nombre n de ces courbes, n étant borné par une constante que lʼon fournit. La courbe de bifurcation de Hopf est incluse dans le graphe de ces courbes.
We give an analytical parametrization of the curves of purely imaginary eigenvalues in the delay-parameter plane of the linearized neural field network equations with space-dependent delays. In order to determine if the rightmost eigenvalue is purely imaginary, we have to compute a finite number of such curves; the number of curves is bounded by a constant for which we give an expression. The Hopf bifurcation curve lies on these curves.
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@article{CRMATH_2011__349_13-14_749_0,
author = {Veltz, Romain},
title = {An analytical method for computing {Hopf} bifurcation curves in neural field networks with space-dependent delays},
journal = {Comptes Rendus. Math\'ematique},
pages = {749--752},
publisher = {Elsevier},
volume = {349},
number = {13-14},
year = {2011},
doi = {10.1016/j.crma.2011.06.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.06.014/}
}
TY - JOUR AU - Veltz, Romain TI - An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays JO - Comptes Rendus. Mathématique PY - 2011 SP - 749 EP - 752 VL - 349 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.06.014/ DO - 10.1016/j.crma.2011.06.014 LA - en ID - CRMATH_2011__349_13-14_749_0 ER -
%0 Journal Article %A Veltz, Romain %T An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays %J Comptes Rendus. Mathématique %D 2011 %P 749-752 %V 349 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.06.014/ %R 10.1016/j.crma.2011.06.014 %G en %F CRMATH_2011__349_13-14_749_0
Veltz, Romain. An analytical method for computing Hopf bifurcation curves in neural field networks with space-dependent delays. Comptes Rendus. Mathématique, Tome 349 (2011) no. 13-14, pp. 749-752. doi : 10.1016/j.crma.2011.06.014. http://www.numdam.org/articles/10.1016/j.crma.2011.06.014/
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