Dynamics of phase oscillators in the Kuramoto model with generalized frequency-weighted coupling

Abstract

We generalize the Kuramoto model for the synchronization transition of globally coupled phase oscillators to populations by incorporating an additional heterogeneity with the coupling strength, where each oscillator pair interacts with different coupling strength weighted by a genera; function of their natural frequency. The expression for the critical coupling can be straightforwardly extended to a generalized explicit formula analytically, and s self-consistency approach is developed to predict the stationary states in the thermodynamic limit. The landau damping effect is further revealed by means of the linear stability analysis and resonance poles theory above the critical threshold which turns to be far more generic. Furthermore, the dimensionality reduction technique of the Ott-Antonsen is implemented to capture the analytical description of relaxation dynamics of the steady states valid on a globally attracting manifold. 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.

arXiv comment8 pages, 1 figures

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Cited by in corpus (5)

• Collective dynamics of heterogeneously and nonlinearly coupled phase oscillators
• Generic criterion for explosive synchronization in heterogeneous phase oscillator populations
• Universal scaling and phase transitions of coupled phase oscillator populations
• Explosive synchronization transition in a ring of coupled oscillators
• A role of asymmetry in linear response of globally coupled oscillator systems