Critical dynamics of the Kuramoto model on sparse random networks

Juhász, Róbert and Kelling, Jeffrey and Ódor, Géza (2019) Critical dynamics of the Kuramoto model on sparse random networks. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (5). pp. 1-13. ISSN 1742-5468

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Abstract

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.

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