Article (Scientific journals)
Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback
Franci, Alessio; Chaillet, Antoine; Pasillas-Lpine, William
2011In Automatica, 47 (6), p. 1193 - 1202
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Keywords :
Deep Brain Stimulation; Kuramoto oscillators; Mean-field feedback; Phase-locking; Deep brain stimulation; Feedback configuration; Feedback gain; Kuramoto models; Mean-field; Neurological disease; Non-linear oscillators; Phase locked state; Robustness properties; Standard assumptions; Control and Systems Engineering; Electrical and Electronic Engineering
Abstract :
[en] Motivated by the recent development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of mean-field feedback and analyze the robustness of its phase-locking with respect to general inputs. Under standard assumptions, this system can be reduced to a modified version of the Kuramoto model of coupled nonlinear oscillators. In the first part of the paper we present an analytical study on the existence of phase-locked solutions under generic interconnection and feedback configurations. In particular we show that, in general, no oscillating phase-locked solutions can co-exist with any non-zero proportional mean-field feedback. In the second part we prove some robustness properties of phase-locked solutions (namely total stability). This general result allows in particular to justify the persistence of practically phase-locked states if sufficiently small feedback gains are applied, and to give explicit necessary conditions on the intensity of a desynchronizing mean-field feedback. Furthermore, the Lyapunov function used in the analysis provides a new characterization of the robust phase-locked configurations in the Kuramoto system with symmetric interconnections. © 2011 Elsevier Ltd. All rights reserved.
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, 91192 Gif-sur-Yvette, France
Chaillet, Antoine;  EECI - L2S - Univ. Paris Sud 11 - Supélec, 91192 Gif-sur-Yvette, France
Pasillas-Lpine, William;  CNRS-L2S, 91192 Gif-sur-Yvette, France
Language :
English
Title :
Existence and robustness of phase-locking in coupled Kuramoto oscillators under mean-field feedback
Publication date :
June 2011
Journal title :
Automatica
ISSN :
0005-1098
Publisher :
Elsevier BV
Volume :
47
Issue :
6
Pages :
1193 - 1202
Peer reviewed :
Peer Reviewed verified by ORBi
European Projects :
FP7 - 257462 - HYCON2 - Highly-complex and networked control systems
Funders :
EU - European Union
CNRS - Centre National de la Recherche Scientifique
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