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

Alexandre Mauroy; Rodolphe Sepulchre

doi:10.1109/CDC.2011.6160621

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

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution

Abstract

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.

Original language	English
Title of host publication	Proceedings of the 50th IEEE Conference on Decision and Control
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	6754-6759
Number of pages	6
ISBN (Print)	9781612848006
DOIs	https://doi.org/10.1109/CDC.2011.6160621
Publication status	Published - 2011
Externally published	Yes
Event	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States Duration: 12 Dec 2011 → 15 Dec 2011

Conference

Conference	2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Country/Territory	United States
City	Orlando, FL
Period	12/12/11 → 15/12/11

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10.1109/CDC.2011.6160621

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title = "Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators",

abstract = "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.",

author = "Alexandre Mauroy and Rodolphe Sepulchre",

year = "2011",

doi = "10.1109/CDC.2011.6160621",

language = "English",

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booktitle = "Proceedings of the 50th IEEE Conference on Decision and Control",

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note = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 ; Conference date: 12-12-2011 Through 15-12-2011",

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Mauroy, A & Sepulchre, R 2011, Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators. in Proceedings of the 50th IEEE Conference on Decision and Control., 6160621, Institute of Electrical and Electronics Engineers Inc., pp. 6754-6759, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160621

Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators. / Mauroy, Alexandre; Sepulchre, Rodolphe.
Proceedings of the 50th IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2011. p. 6754-6759 6160621.

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Conference contribution

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AU - Sepulchre, Rodolphe

PY - 2011

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N2 - 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.

AB - 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.

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M3 - Conference contribution

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BT - Proceedings of the 50th IEEE Conference on Decision and Control

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Y2 - 12 December 2011 through 15 December 2011

ER -

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

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