Pazó, DiegoMontbrió, Ernest, 1974-2016-02-192016-02-192014Pazo 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.4.011009.0031-899Xhttp://hdl.handle.net/10230/25902Large 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.application/pdfengPublished 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 DOIinfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1103/PhysRevX.4.011009.info:eu-repo/semantics/openAccess