Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators

Collective behavior; Continuum model; Finite dimensional; Finite population; Integrate and fires; Local stability; Pulse-coupled oscillators; Stability analysis; Stability results; Weak couplings; Continuum mechanics; Stability

Abstract :

[en] In this paper, we investigate the behavior of pulse-coupled integrate-and-fire oscillators. Because the stability analysis of finite populations is intricate, we investigate stability results in the approximation of infinite populations. In addition to recovering known stability results of finite populations, we also obtain new stability results for infinite populations. In particular, under a weak coupling assumption, we solve for the continuum model a conjecture still prevailing in the finite dimensional case. © 2011 IEEE.

Disciplines :

Engineering, computing & technology: Multidisciplinary, general & others
Mathematics

Author, co-author :

Mauroy, Alexandre ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators

Publication date :

2011

Event name :

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

Event place :

Orlando, FL, United States

Event date :

12 December 2011 through 15 December 2011

Audience :

International

Journal title :

Proceedings of the IEEE Conference on Decision and Control

ISSN :

0191-2216

Pages :

6754-6759

Peer reviewed :

Peer reviewed

Available on ORBi :

since 03 April 2014

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Bibliography

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