Analysis of Jansen’s model of a single cortical column
نویسندگان
چکیده
In this report we present a mathematical analysis of a simple model of a cortical column. We first recall some known biological facts about cortical columns. We then present a mathematical model of such a column, developed by a number of people including Lopes Da Silva, Jansen, Rit. Finally we analyze some aspects of its behaviour in the framework of the theory of dynamical systems using bifurcation theory and the software package XPP-Aut developed by B. Ermentrout. This mathematical approach leads us to a compact representation of the model that allows to finally discuss its adequacy with biology. Key-words: cortical columns, EEG, modeling, dynamical systems, bifurcations, XPP-Aut ∗ This work was partially supported by Elekta Instrument AB. Analyse du modèle de colonne corticale de Jansen Résumé : Nous présentons dans ce rapport l’analyse d’un modèle simple de colonne corticale. Nous commençons par rappeler quelques faits connus sur ces colonnes. Nous présentons ensuite un modèle mathématique de colonne, développé par un certain nombre d’auteurs dont Lopes Da Silva, Jansen, Rit. Nous analysons ensuite quelques aspects de son comportement en utilisant la théorie des bifurcations et le logiciel XPP-Aut développé par B. Ermentrout. Cette étude mathématique nous a donné une vision suffisamment compacte du modèle pour pouvoir en critiquer l’adéquation avec la biologie dans la discussion finale. Mots-clés : colonne corticale, EEG, modélisation, système dynamique, bifurcation, XPP-Aut Cortical column modeling 3
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تاریخ انتشار 2017