Synchronization of phase oscillators with frequency-weighted coupling

Abstract

Recently, the first-order synchronization transition has been studied in systems of coupled phase oscillators. In this paper, we propose a framework to investigate the synchronization in the frequency-weighted Kuramoto model with all-to-all couplings. A rigorous mean-field analysis is implemented to predict the possible steady states. Furthermore, a detailed linear stability analysis proves that the incoherent state is only neutrally stable below the synchronization threshold. Nevertheless, interestingly, the amplitude of the order parameter decays exponentially (at least for short time) in this regime, resembling the Landau damping effect in plasma physics. Moreover, the explicit expression for the critical coupling strength is determined by both the mean-field method and linear operator theory. The mechanism of bifurcation for the incoherent state near the critical point is further revealed by the amplitude expansion theory, which shows that the oscillating standing wave state could also occur in this model for certain frequency distributions. Our theoretical analysis and numerical results are consistent with each other, which can help us understand the synchronization transition in general networks with heterogenous couplings.

16 pages, 2 figures

References in corpus (16)

• Explosive Synchronization Transitions in Scale-free Networks
• Explosive synchronization in adaptive and multilayer networks
• Thermodynamic limit of the first-order phase transition in the Kuramoto model
• Explosive first-order transition to synchrony in networked chaotic oscillators
• Amplitude Expansions for Instabilities in Populations of Globally-Coupled Oscillators
• Kuramoto model with frequency-degree correlations on complex networks
• Explosive transitions to synchronization in networked phase oscillators
• Explosive synchronization in weighted complex networks
• Critical behavior of the relaxation rate, the susceptibility, and a pair correlation function in the Kuramoto model on scale-free networks
• Disorder induces explosive synchronization
• Explosive oscillation death in coupled Stuart-Landau oscillators
• Mean Field and Mean Ensemble Frequencies of a System of Coupled Oscillators
• Low-dimensional behavior of Kuramoto model with inertia in complex networks
• Explosive synchronization with partial degree-frequency correlation
• Analysis of cluster explosive synchronization in complex networks
• Synchronization of phase oscillators with heterogeneous coupling: A solvable case