doi:10.1103/PhysRevE.100.042302engPeron, ThomasMessias F De Resende, BrunoMata, Angelica S.Rodrigues, Francisco A.Moreno, YamirOnset of synchronization of Kuramoto oscillators in scale-free networksART-2019-114918Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent 2<¿=3, in line with what has been observed for other dynamical processes in such networks. For ¿>3, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.2019http://zaguan.unizar.es/record/8634310.1103/PhysRevE.100.042302http://zaguan.unizar.es/record/86343oai:zaguan.unizar.es:86343info:eu-repo/grantAgreement/ES/DGA/E36-17Rinfo:eu-repo/grantAgreement/ES/MINECO/FIS2017-87519-PPHYSICAL REVIEW E 100, 4 (2019), 042302 1-8All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess