Synchronization transition in Sakaguchi-Kuramoto model on complex networks with partial degree-frequency correlation

We investigate transition to synchronization in the Sakaguchi-Kuramoto (SK) model on complex networks analytically as well as numerically. Natural frequencies of a percentage (f) of higher degree nodes of the network are assumed to be correlated with their degrees and that of the remaining nodes are drawn from some standard distribution, namely, Lorentz distribution. The effects of variation of f and phase frustration parameter alpha on transition to synchronization are investigated in detail. Self-consistent equations involving critical coupling strength (lambda(c)) and group angular velocity (Omega(c)) at the onset of synchronization have been derived analytically in the thermodynamic limit. For the detailed investigation, we considered the SK model on scale-free (SF) as well as Erdos-Renyi (ER) networks. Interestingly, explosive synchronization (ES) has been observed in both networks for different ranges of values of alpha and f. For SF networks, as the value off is set within 10% <= f <= 70%, the range of the values of alpha for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case when scaling exponent gamma < 3. ES is also observed in SF networks with gamma > 3, which is never observed in fully degree-frequency correlated environment. On the other hand, for random networks, ES observed is in a narrow window of alpha when the value of f is taken within 30% <= f <= 50%. In all the cases, critical coupling strengths for transition to synchronization computed from the analytically derived self-consistent equations show a very good agreement with the numerical results. Finally, we observe ES in the metabolic network of the roundworm Caenorhabditis elegans in partially degree-frequency correlated environment. Published under license by AIP Publishing.