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

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 Erdős-Rényi (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 $10\%\le f\le 70\%$, 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 $30\%\le f\le 50\%$. 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.

7 pages, 5 figures

References in corpus (14)

• Synchronization in complex networks
• The Kuramoto model in complex networks
• Explosive Synchronization Transitions in Scale-free Networks
• Explosive synchronization in adaptive and multilayer networks
• Explosive transitions in complex networks' structure and dynamics: percolation and synchronization
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Explosive first-order transition to synchrony in networked chaotic oscillators
• Kuramoto model with frequency-degree correlations on complex networks
• Disorder induces explosive synchronization
• Shear diversity prevents collective synchronization
• Explosive synchronization with partial degree-frequency correlation
• Effects of degree-frequency correlations on network synchronization: universality and full phase-locking
• Transition to synchrony in degree-frequency correlated Sakaguchi-Kuramoto model
• The emergence and analysis of Kuramoto-Sakaguchi-like models as an effective description for the dynamics of coupled Wien-bridge oscillators

Cited by in corpus (4)

• Generalized frustration in the multidimensional Kuramoto model
• Mean-field theory for double-well systems on degree-heterogeneous networks
• Optimizing synchronization in multiplex networks of phase oscillators
• Explosive synchronization in networks of Type-I neurons with electrical synapses