Kuramoto model with frequency-degree correlations on complex networks

Coutinho, B. C.; Goltsev, A. V.; Dorogovtsev, S. N.; Mendes, J. F. F.
We study the Kuramoto model on complex networks, in which natural frequencies of phase oscillators and the vertex degrees are correlated. Using the annealed network approximation and numerical simulations we explore a special case in which the natural frequencies of the oscillators and the vertex degrees are linearly coupled. We find that in uncorrelated scale-free networks with the degree distribution exponent \$2 cal simulations for Erd$\backslash$H\{o\}s--R$\backslash$'\{e\}nyi and scale-free networks, we demonstrate that the annealed network approach is accurate if the the mean degree and size of the network are sufficiently large. We also study analytically and numerically the Kuramoto model on star graphs and find that if the natural frequency of the central oscillator is sufficiently large in comparison to the average frequency of its neighbors, then synchronization emerges as a result of a first-order phase transition. This shows that oscillators sitting at hubs in a network may generate a discontinuous synchronization transition.
Research areas:
Year:
2013
Type of Publication:
Article
Journal:
Physical Review E
Volume:
87
Number:
3
Pages:
32106
Month:
March
ISSN:
1539-3755
DOI:
10.1103/PhysRevE.87.032106
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