Hypothèse de synchronisation dans le modèle de Winfree
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Université Yahia Fares de Médéa | |
| dc.contributor.author | OUKIL, W | |
| hal.structure.identifier | Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger] [USTHB] | |
| dc.contributor.author | KESSI, A | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | THIEULLEN, Ph | |
| dc.date.accessioned | 2024-04-04T03:14:24Z | |
| dc.date.available | 2024-04-04T03:14:24Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194053 | |
| dc.description.abstractEn | We consider $N$ oscillators coupled by a mean field as in the Winfree model. The model is governed by two parameters: the coupling strength $\kappa$ and the spectrum width $\gamma$ of the frequencies of each oscillator. In the uncoupled regime, $\kappa=0$, each oscillator possesses its own natural frequency, and the difference between the phases of any two oscillators grows linearly in time. We say that $N$ oscillators are synchronized if the difference between any two phases is uniformly bounded in time. We identify a new hypothesis for the existence of synchronization. The domain in $(\gamma,\kappa)$ of synchronization contains coupling values that are both weak and strong. Moreover the domain is independent of the number of oscillators and the distribution of the frequencies. We give a numerical counter-example which shows that this hypothesis is necessary for the existence of synchronization. | |
| dc.language.iso | en | |
| dc.subject.en | desynchronization | |
| dc.subject.en | synchronization | |
| dc.subject.en | Winfree Model | |
| dc.subject.en | Coupled oscillators | |
| dc.subject.en | periodic orbit | |
| dc.title | Hypothèse de synchronisation dans le modèle de Winfree | |
| dc.title.en | Synchronization hypothesis in the Winfree model | |
| dc.title.en | Synchronization in Winfree model with N oscillators | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Systèmes dynamiques [math.DS] | |
| dc.identifier.arxiv | 1507.06061 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01175759 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01175759v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.title=Hypoth%C3%A8se%20de%20synchronisation%20dans%20le%20mod%C3%A8le%20de%20Winfree&rft.atitle=Hypoth%C3%A8se%20de%20synchronisation%20dans%20le%20mod%C3%A8le%20de%20Winfree&rft.au=OUKIL,%20W&KESSI,%20A&THIEULLEN,%20Ph&rft.genre=preprint |
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