2005/09/30 by Diego Pazó, Diego Pazo · 1 citation
Computer Science · Engineering · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research #Theoretical and Computational Physics #nlin.AO
paper · pdf · doi:10.1103/physreve.72.046211
published as Physical Review E 72, 046211 (2005) · 6 pages
openalex publication_date 2005/10/18 · arxiv created 2005/10/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In the Kuramoto model, a uniform distribution of the natural frequencies leads to a first-order (i.e., discontinuous) phase transition from incoherence to synchronization, at the critical coupling parameter K(c). We obtain the asymptotic dependence of the order parameter above criticality: r-r(c)alpha(K - K(c))(2/3). For a finite population, we demonstrate that the population size N may be included into a self-consistency equation relating r and K in the synchronized state. We analyze the convergence to the thermodynamic limit of two alternative schemes to set the natural frequencies. Other frequency distributions different from the uniform one are also considered.