Exponential asymptotic stability of the Kuramoto system with periodic natural frequencies and constant inertia
type: Item
instance of: scholarly article
title: Exponential asymptotic stability of the Kuramoto system with periodic natural frequencies and constant inertia
author: Sun-Ho Choi
author: Hyowon Seo
published in: Journal of Nonlinear Science
publication date: 2022-12-08T00:00:00Z
review text: The authors consider the system \[ I\ddot{\theta}_i+\dot{\theta}_i=\omega_i+\frac{K}{N}\sum_{k=1}^N\sin{(\theta_k-\theta_i)} \] modelling a network of \(N\) all-to-all coupled Kuramoto phase oscillators with inertia. The frequencies \(\{\omega_i\}\) are all \(T\)-periodic in time and there is an upper bound on the absolute value of the difference between any two oscillator's frequencies, at any time. The main result proved is that, under certain assumptions, the asymptotic-in-time solution for each oscillator consists of the sum of three terms. The first is a macroscopic phase, common to all oscillators and determined by initial values of the oscillators and frequencies. The second is a ``standing wave'' independent of initial conditions for which the difference between any two phases is \(T\)-periodic. The third is a term which decays exponentially in time. A number of simulations are shown which illustrate some of the analytical results.
reviewed by: Carlo Laing
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 34D06
zbMATH DE Number: 7628876
zbMATH Keywords: Kuramoto model
zbMATH Keywords: time-periodic natural frequency
zbMATH Keywords: inertia
zbMATH Keywords: mean-centered-periodic solution
zbMATH Keywords: exponential asymptotic stability
MaRDI profile type: Publication
full work available at URL: s00332-022-09870-1
OpenAlex ID: W4310276480
cites work: Emergent behaviors of a holonomic particle system on a sphere
cites work: Complete Entrainment of Lohe Oscillators under Attractive and Repulsive Couplings
cites work: Emergent behaviors of quantum Lohe oscillators with all-to-all coupling
cites work: Synchronization in a Power Balance System With Inertia and Nonlinear Derivatives
cites work: Asymptotic behavior of the Kuramoto system with periodic natural frequency
cites work: Complete synchronization of Kuramoto oscillators with finite inertia
cites work: Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model
cites work: Practical quantum synchronization for the Schrödinger–Lohe system
cites work: On the chaos synchronization phenomena
cites work: Frequency Entrainment of a Forced van der Pol Oscillator
cites work: Kuramoto model of synchronization: equilibrium and nonequilibrium aspects
cites work: On the complete synchronization of the Kuramoto phase model
cites work: Q4360293
cites work: Non-Abelian Kuramoto models and synchronization
DOI: 10.1007/S00332-022-09870-1
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description: scientific article; zbMATH DE number 7628876