Nontrivial standing wave state in frequency-weighted Kuramoto model

TL;DR

This paper investigates a frequency-weighted Kuramoto model with a uniform distribution, revealing a novel nonstationary standing wave state characterized by locked average frequencies but non-frequency-locked oscillators, supported by bifurcation analysis and simulations.

Contribution

It introduces and characterizes a new nontrivial standing wave state in the frequency-weighted Kuramoto model, supported by theoretical and numerical analysis.

Findings

Identification of a nonstationary standing wave state

Observation of two first-order transitions in synchronization

Derivation of critical coupling strength via linear stability analysis

Abstract

Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two first-order transitions in both the forward and backward directions. Apart from the trivial phase-locked state, a novel nonstationary coherent state, i.e., a nontrivial standing wave state is observed and characterized. In this state, oscillators inside the coherent clusters are not frequency-locked as they would be in the usual standing wave state. Instead, their average frequencies are locked to a constant. The critical coupling strength from the incoherent state to the nontrivial standing wave state can be obtained by performing linear stability analysis. The theoretical results are supported by the numerical simulations.