Existence of phase-locking in the Kuramoto system under mean-field feedback

Franci, Alessio; Pasillas-Lépine, W; Chaillet, A

doi:10.3182/20110828-6-IT-1002.02141

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Existence of phase-locking in the Kuramoto system under mean-field feedback

Franci, Alessio; Pasillas-Lépine, W; Chaillet, A

2011 • In IFAC Proceedings Volumes (IFAC-PapersOnline)

Peer reviewed

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https://hdl.handle.net/2268/320271

DOI
10.3182/20110828-6-IT-1002.02141

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Keywords :

Deep brain stimulation; Kuramoto oscillators; Mean-field feedback; Phase-locking; Feedback; Locks (fasteners); Neurosurgery; Coupled nonlinear oscillators; Implicit function theorem; Mean field; Neurological disease; Standard assumptions; Microwave oscillators

Abstract :

[en] Motivated by the development of Deep Brain Stimulation (DBS) for neurological diseases, we study a network of interconnected oscillators under the influence of a proportional mean-field feedback. 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 show that, in general, no oscillating phase-locked solution can co-exist with any non-zero feedback gain. In the second part we propose a new characterization of phase-locking between Kuramoto oscillators. In particular we derive a fixed point equation for the Kuramoto system under mean-field feedback and we show how, generically, the "standard" (with zero feedback gain) Kuramoto fixed point equation is locally invertible in terms of the implicit function theorem. © 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

Pasillas-Lépine, W; CNRS, L2S, France

Chaillet, A; EECI, L2S, France

Language :

English

Title :

Existence of phase-locking in the Kuramoto system under mean-field feedback

Publication date :

2011

Event name :

IFAC World Congress 2011

Event date :

2011

Main work title :

IFAC Proceedings Volumes (IFAC-PapersOnline)

Publisher :

IFAC Secretariat

Peer reviewed :

Peer reviewed

Available on ORBi :

since 02 July 2024

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