Onset of synchronization of Kuramoto oscillators in scale-free networks.
PERON, Thomas; RESENDE, Bruno Messias Farias de; MATA, Angélica S.; RODRIGUES, Francisco Aparecido; MORENO, Yamir.
PERON, Thomas; RESENDE, Bruno Messias Farias de; MATA, Angélica S.; RODRIGUES, Francisco Aparecido; MORENO, Yamir.
Abstract: Despite 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.
@article={002969401,author = {PERON, Thomas; RESENDE, Bruno Messias Farias de; MATA, Angélica S.; RODRIGUES, Francisco Aparecido; MORENO, Yamir.},title={Onset of synchronization of Kuramoto oscillators in scale-free networks},journal={Physical Review E},note={v. 100, n. 4, p. 042302-1-042302-8},year={2019}}