Synchronization of oscillators in a Kuramoto-type model with generic coupling

Abstract

We study synchronization properties of coupled oscillators on networks that allow description in terms of global mean field coupling. These models generalize the standard Kuramoto-Sakaguchi model, allowing for different contributions of oscillators to the mean field and to different forces from the mean field on oscillators. We present the explicit solutions of self-consistency equations for the amplitude and frequency of the mean field in a parametric form, valid for noise-free and noise-driven oscillators. As an example we consider spatially spreaded oscillators, for which the coupling properties are determined by finite velocity of signal propagation.

arXiv comment15 pages, 7 figures

References in corpus (7)

• Stationary and Traveling Wave States of the Kuramoto Model with an Arbitrary Distribution of Frequencies and Coupling Strengths
• Hierarchical Synchrony of Phase Oscillators in Modular Networks
• Glassy states and superrelaxation in populations of coupled phase oscillators
• Shear diversity prevents collective synchronization
• Collective synchronization in the presence of reactive coupling and shear diversity
• Synchronization of phase oscillators with heterogeneous coupling: A solvable case
• The Kuramoto model with distributed shear

Cited by in corpus (12)

• Coupling functions: Universal insights into dynamical interaction mechanisms
• A note on dynamical models on random graphs and Fokker-Planck equations
• Solitary States and Partial Synchrony in Oscillatory Ensembles with Attractive and Repulsive Interactions
• Collective dynamics in two populations of noisy oscillators with asymmetric interactions
• Dynamics of phase oscillators in the Kuramoto model with generalized frequency-weighted coupling
• Star-type oscillatory networks with generic Kuramoto-type coupling: a model for "Japanese drums synchrony"
• Hierarchy of exact low-dimensional reductions for populations of coupled oscillators
• Erosion of synchronization: Coupling heterogeneity and network structure
• Dynamics of oscillator populations globally coupled with distributed phase shifts
• Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings
• Dynamics of large oscillator populations with random interactions
• Multiple-parameter bifurcation analysis in a Kuramoto model with time delay and distributed shear