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Toward oscillations inhibition by mean-field feedback in Kuramoto oscillators
Franci, Alessio; Chaillet, A.; Bezzaoucha, S.
2011In Proceedings of the 18th IFAC World Congress
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Keywords :
Deep brain stimulation; Kuramoto oscillators; Mean-field feedback; Phase-locking; All to alls; Hyperbolicity; Mean field; Neurological disease; Output feedback; Control and Systems Engineering; General Economics, Econometrics and Finance
Abstract :
[en] This note shows that the oscillations in a network of all-to-all coupled Kuramoto oscillators can be inhibited by a scalar output feedback. More precisely, by injecting an input proportional to the oscillators mean-field, a set of isolated equilibria is shown to be almost globally attractive when natural frequencies are zero. The normal hyperbolicity of all relevant equilibria let us conjecture that this property persists in the presence of natural frequencies that are sufficiently small with respect to the coupling gain. This work constitutes a first step in the direction of testing the possible neuronal inhibition arising in deep brain stimulation treatment for neurological diseases. © 2011 IFAC.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Franci, Alessio  ;  Université de Liège - ULiège > Département d'électricité, électronique et informatique (Institut Montefiore) > Brain-Inspired Computing ; Univ. Paris Sud 11, L2S, Supélec, Gif sur Yvette, 91192, France
Chaillet, A.;  L2S, EECI, Supélec, France
Bezzaoucha, S.;  L2S, Ecole Polytechnique, LIX, France
Language :
English
Title :
Toward oscillations inhibition by mean-field feedback in Kuramoto oscillators
Publication date :
2011
Event name :
IFAC World Congress
Event date :
2011
Main work title :
Proceedings of the 18th IFAC World Congress
Publisher :
IFAC Secretariat
ISBN/EAN :
978-3-902661-93-7
Peer reviewed :
Peer reviewed
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since 26 May 2023

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