Synchronization scenarios in the Winfree model of coupled oscillators

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• dc.contributor.author Gallego, Rafael
• dc.contributor.author Montbrió, Ernest, 1974-
• dc.contributor.author Pazó, Diego
• dc.date.accessioned 2021-06-08T09:48:14Z
• dc.date.available 2021-06-08T09:48:14Z
• dc.date.issued 2017
• dc.description.abstract Fifty years ago Arthur Winfree proposed a deeply influential mean-field model for the collective synchronization of large populations of phase oscillators. Here we provide a detailed analysis of the model for some special, analytically tractable cases. Adopting the thermodynamic limit, we derive an ordinary differential equation that exactly describes the temporal evolution of the macroscopic variables in the Ott-Antonsen invariant manifold. The low-dimensional model is then thoroughly investigated for a variety of pulse types and sinusoidal phase response curves (PRCs). Two structurally different synchronization scenarios are found, which are linked via the mutation of a Bogdanov-Takens point. From our results, we infer a general rule of thumb relating pulse shape and PRC offset with each scenario. Finally, we compare the exact synchronization threshold with the prediction of the averaging approximation given by the Kuramoto-Sakaguchi model. At the leading order, the discrepancy appears to behave as an odd function of the PRC offset.
• dc.description.sponsorship We acknowledge support by MINECO (Spain) under Projects No. FIS2014-59462-P, No. FIS2016-74957-P, No. PSI2016-75688-P, and No. PCIN-2015-127. E.M. and D.P. also acknowledge support by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 642563.
• dc.format.mimetype application/pdf
• dc.identifier.citation Gallego R, Montbrió E, Pazó D. Synchronization scenarios in the Winfree model of coupled oscillators. Phys Rev E. 2017;96(4):042208. DOI: 10.1103/PhysRevE.96.042208
• dc.identifier.doi http://dx.doi.org/10.1103/PhysRevE.96.042208
• dc.identifier.issn 1539-3755
• dc.identifier.uri http://hdl.handle.net/10230/47797
• dc.language.iso eng
• dc.publisher American Physical Society
• dc.relation.ispartof Physical Review E. 2017;96(4):042208
• dc.relation.projectID info:eu-repo/grantAgreement/EC/H2020/642563
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/FIS2014-59462-P
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/FIS2016-74957-P
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/PSI2016-75688-P
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/PCIN-2015-127
• dc.rights © American Physical Society. Published article available at https://doi.org/10.1103/PhysRevE.96.042208
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.title Synchronization scenarios in the Winfree model of coupled oscillators
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion