Low-dimensional dynamics of populations of pulse-coupled oscillators

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• dc.contributor.author Pazó, Diegoca
• dc.contributor.author Montbrió, Ernest, 1974-ca
• dc.date.accessioned 2016-02-19T07:43:57Z
• dc.date.available 2016-02-19T07:43:57Z
• dc.date.issued 2014
• dc.description.abstract Large communities of biological oscillators show a prevalent tendency to self-organize in time. This/ncooperative phenomenon inspired Winfree to formulate a mathematical model that originated the theory of/nmacroscopic synchronization. Despite its fundamental importance, a complete mathematical analysis of the/nmodel proposed by Winfree/n—/nconsisting of a large population of all-to-all pulse-coupled oscillators/n—/nis/nstill missing. Here, we show that the dynamics of the Winfree model evolves into the so-called Ott-/nAntonsen manifold. This important property allows for an exact description of this high-dimensional/nsystem in terms of a few macroscopic variables, and also allows for the full investigation of its dynamics./nWe find that brief pulses are capable of synchronizing heterogeneous ensembles that fail to synchronize/nwith broad pulses, especially for certain phase-response curves. Finally, to further illustrate the potential of/nour results, we investigate the possibility of/n“/nchimera/n”/nstates in populations of identical pulse-coupled/noscillators. Chimeras are self-organized states in which the symmetry of a population is broken into a/nsynchronous and an asynchronous part. Here, we derive three ordinary differential equations describing/ntwo coupled populations and uncover a variety of chimera states, including a new class with chaotic/ndynamics.ca
• dc.description.sponsorship We thank Juan M. López for a critical reading of the manuscript, Arkady Pikovsky for interesting discussions, and John Rinzel for pointing us to Ref. [7]. D. P. acknowl-edges support from Cantabria International Campus and the Ramón y Cajal program of MINECO (Spain). We acknowl-edge support from the Spanish research Projects No. FIS2009-12964-C05-05 and No. SAF2010-16085.
• dc.format.mimetype application/pdfca
• dc.identifier.citation Pazo D, Montbrio E. Low-dimensional dynamics of populations of pulse-coupled oscillators. Physical Review. 2014;4(1):011009-1-011009-7. DOI: 10.1103/PhysRevX.4.011009.
• dc.identifier.doi http://dx.doi.org/10.1103/PhysRevX.4.011009.
• dc.identifier.issn 0031-899X
• dc.identifier.uri http://hdl.handle.net/10230/25902
• dc.language.iso engca
• dc.publisher American Physical Societyca
• dc.relation.ispartof Physical Review. 2014;4(1):011009-1-011009-7
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/FIS2009-12964
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/SAF2010-16085
• dc.rights Published by the American Physical Society under the terms of/nthe Creative Commons Attribution 3.0 License. Further distri-/nbution of this work must maintain attribution to the author(s) and/nthe published articles title, journal citation, and DOIca
• dc.rights.accessRights info:eu-repo/semantics/openAccessca
• dc.rights.uri http://creativecommons.org/licenses/by/3.0/ca
• dc.title Low-dimensional dynamics of populations of pulse-coupled oscillatorsca
• dc.type info:eu-repo/semantics/articleca
• dc.type.version info:eu-repo/semantics/publishedVersionca