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Synchronization scenarios in the Winfree model of coupled oscillators

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. © 2017 American Physical Society.

 Fuente: Phys. Rev. E 96, 042208

Editorial: American Physical Society

 Fecha de publicación: 01/10/2017

Nº de páginas: 11

Tipo de publicación: Artículo de Revista

 DOI: 10.1103/PhysRevE.96.042208

ISSN: 1539-3755,1550-2376,2470-0045,2470-0053

Proyecto español: FIS2014-59462-P; FIS2016-74957-P; PSI2016-75688-P; CIN-2015-127

Url de la publicación: https://doi.org/10.1103/PhysRevE.96.042208