Critical dynamics of the Kuramoto model on sparse random networks
Critical dynamics of the Kuramoto model on sparse random networks
Juhász, R.; Kelling, J.; Ódor, G.
We consider the Kuramoto model on sparse random networks such as the Erdős-Rényi graph or its combination with a regular two-dimensional lattice and study the dynamical scaling behavior of the model at the synchronization transition by large-scale, massively parallel numerical integration. By this method, we obtain an estimate of critical coupling strength more accurate than obtained earlier by finite-size scaling of the stationary order parameter. Our results confirm the compatibility of the correlation-size and the temporal correlation-length exponent with the mean-field universality class. However, the scaling of the order parameter exhibits corrections much stronger than those of the Kuramoto model with all-to-all coupling, making thereby an accurate estimate of the order-parameter exponent hard. We find furthermore that, as a qualitative difference to the model with all-to-all coupling, the effective critical exponents involving the order-parameter exponent, such as the effective decay exponent characterizing the critical desynchronization dynamics show a non-monotonic approach toward the asymptotic value. In the light of these results, the technique of finite-size scaling of limited size data for the Kuramoto model on sparse graphs has to be treated cautiously.
Keywords: Networks; Kuramoto Model; Synchronization
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Contribution to WWW
https://arxiv.org/abs/1902.10422 -
Journal of Statistical Mechanics: Theory and Experiment 5(2019), 053403
DOI: 10.1088/1742-5468/ab16c3
Cited 9 times in Scopus
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Permalink: https://www.hzdr.de/publications/Publ-28954
Publ.-Id: 28954