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

Research output: Contribution in Book/Catalog/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationProceedings of the 50th IEEE Conference on Decision and Control
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages6754-6759
Number of pages6
ISBN (Print)9781612848006
DOIs
Publication statusPublished - 2011
Externally publishedYes
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: 12 Dec 201115 Dec 2011

Conference

Conference2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1115/12/11

Fingerprint

Collective Behavior
Local Stability
Coupled Oscillators
Finite Population
Weak Coupling
Continuum Model
Stability Analysis
Integrate
Fires
Approximation

Cite this

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 (pp. 6754-6759). [6160621] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2011.6160621
Mauroy, Alexandre ; Sepulchre, Rodolphe. / Local stability results for the collective behaviors of infinite populations of pulse-coupled oscillators. Proceedings of the 50th IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2011. pp. 6754-6759
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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 proceedingConference contribution

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Mauroy A, Sepulchre R. 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. Institute of Electrical and Electronics Engineers Inc. 2011. p. 6754-6759. 6160621 https://doi.org/10.1109/CDC.2011.6160621