2007/05/03 by Floriana Giannuzzi, F. Giannuzzi, Daniele Marinazzo +5
Computer Science · Engineering · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research #Theoretical and Computational Physics #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.75.051104
published as Physical Review E 75, 051104 (2007) · 9 pages, 3 figures
openalex publication_date 2007/05/03 · arxiv created 2008/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the phase diagram of a generalized Winfree model. The modification is such that the coupling depends on the fraction of synchronized oscillators, a situation which has been noted in some experiments on coupled Josephson junctions and mechanical systems. We let the global coupling k be a function of the Kuramoto order parameter r through an exponent z such that z=1 corresponds to the standard Winfree model, z<1 strengthens the coupling at low r (low amount of synchronization), and at z>1 , the coupling is weakened for low r . Using both analytical and numerical approaches, we find that z controls the size of the incoherent phase region and that one may make the incoherent behavior less typical by choosing z<1 . We also find that the original Winfree model is a rather special case; indeed, the partial locked behavior disappears for z>1 . At fixed k and varying gamma , the stability boundary of the locked phase corresponds to a transition that is continuous for z<1 and first order for z>1 . This change in the nature of the transition is in accordance with a previous study of a similarly modified Kuramoto model.