Renormalization Group Approach to Oscillator Synchronization

Abstract

We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic frequencies and coupling strengths. The results are compared with numerical simulations of the chain dynamics and good agreement in several characteristics is found. We apply the renormalization group and simulations to Lorentzian distributions of intrinsic frequencies and couplings and investigate the statistics of the resultant cluster sizes and frequencies, as well as the dependence of the characteristic cluster length upon parameters of these Lorentzian distributions.

13 pages, 7 figures: 8 figure files in *.eps format and one *.tex file

References in corpus (4)

• Phase transition of one dimensional bosons with strong disorder
• Distributions of gaps and end-to-end correlations in random transverse-field Ising spin chains
• Synchronization in disordered Josephson junction arrays: Small-world connections and the Kuramoto model
• The insulating phases and superfluid-insulator transition of disordered boson chains

Cited by in corpus (15)

• Quantum Synchronization of Two Ensembles of Atoms
• Entanglement tongue and quantum synchronization of disordered oscillators
• Strong Disorder RG approach - a short review of recent developments
• Synchronization in interdependent networks
• Vortices and the entrainment transition in the 2D Kuramoto model
• Random elastic networks : strong disorder renormalization approach
• Universality in the one-dimensional chain of phase-coupled oscillators
• Network Renormalization
• Comparing the Locking Threshold for Rings and Chains of Oscillators
• Emulating the local Kuramoto model with an injection-locked photonic crystal laser array
• Koopman analysis in oscillator synchronization
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Criticality & Deep Learning II: Momentum Renormalisation Group
• Large Disorder Renormalization Group Study of the Anderson Model of Localization
• Spatio-temporal patterns of active epigenetic turnover