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

TL;DR

This paper analyzes how partial degree-frequency correlation affects synchronization transitions, including explosive synchronization, in the Sakaguchi-Kuramoto model on complex networks through analytical and numerical methods.

Contribution

It introduces a self-consistent analytical framework for the Sakaguchi-Kuramoto model with partial correlation and explores the conditions for explosive synchronization on different network types.

Findings

Explosive synchronization occurs under certain conditions of partial correlation and phase frustration.

The analytical predictions of critical coupling match numerical simulations closely.

Partial correlation extends the parameter range for explosive synchronization in scale-free networks.

Abstract

We investigate transition to synchronization in 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 Lorenz 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 SK model on scale-free as well as Erd\H{o}s-R\'{e}nyi (ER) networks. Interestingly explosive synchronization (ES) has been observed in both the networks for different ranges of values of $\alpha$ and $f$. For scale-free networks, as the value of $f$ is set within $10\% \leq f \leq 70\%$, the range of the values of $\alpha$ for existence of the ES is greatly enhanced compared to the fully degree-frequency correlated case. On the other hand, for random networks, ES observed in a narrow window of $\alpha$ when the value of $f$ is taken within $30\% \leq f \leq 50\%$. 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.