On the onset of synchronization of Kuramoto oscillators in scale-free networks

Abstract

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2<\gamma \le 3$, in line with what has been observed for other dynamical processes in such networks. For $\gamma >3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators.

References in corpus (29)

• Synchronization in complex networks
• The Kuramoto model in complex networks
• Generation of uncorrelated random scale-free networks
• Thresholds for epidemic spreading in networks
• The onset of synchronization in large networks of coupled oscillators
• Nature of the epidemic threshold for the susceptible-infected-susceptible dynamics in networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Synchronization of Kuramoto Oscillators in Scale-Free Networks
• Frequency synchronization in random oscillator network
• Contact processes on random graphs with power law degree distributions have critical value 0
• Cluster Explosive Synchronization in Complex Networks
• Non mean-field behavior of the contact process on scale-free networks
• Hysteretic transitions in the Kuramoto model with inertia
• Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
• Synchronization transition in scale-free networks: Clusters of synchrony
• Disease Localization in Multilayer Networks
• Heterogeneous pair-approximation for the contact process on complex networks
• Nonequilibrium phase transitions and finite size scaling in weighted scale-free networks
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks
• Collective versus hub activation of epidemic phases on networks
• Bifurcations and singularities for coupled oscillators with inertia and frustration
• Finite-size scaling of synchronized oscillation on complex networks
• Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
• Synchronization Dynamics in the Presence of Coupling Delays and Phase Shifts
• Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
• Power grid stability under perturbation of single nodes: Effects of heterogeneity and internal nodes
• Nature of synchronization transitions in random networks of coupled oscillators
• Link-disorder fluctuation effects on synchronization in random networks
• Critical dynamics of the Kuramoto model on sparse random networks

Cited by in corpus (8)

• Collective dynamics of random Janus oscillator networks
• Social Network Heterogeneity Promotes Depolarization of Multidimensional Correlated Opinions
• Node differentiation dynamics along the route to synchronization in complex networks
• Mesoscopic model reduction for the collective dynamics of sparse coupled oscillator networks
• Emergent synchrony in oscillator networks with adaptive arbitrary-order interactions
• Global hierarchy vs. local structure: spurious self-feedback in scale-free networks
• Adversarial control of synchronization in complex oscillator networks
• Mean-field theory of vector spin models on networks with arbitrary degree distributions