High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally
(2020) In Automatica 113.- Abstract
The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto models where each oscillator lives on the n-sphere or SO(n). These manifolds are special cases of the compact, real Stiefel manifold St(p,n). Using tools from optimization and control theory, we prove that the generalized Kuramoto model on St(p,n) converges to a synchronized state for any connected graph and from almost all initial conditions provided (p,n) satisfies p≤2/3n−1 and all oscillator frequencies are equal. This result could not have been predicted based on knowledge of the Kuramoto model in... (More)
The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto models where each oscillator lives on the n-sphere or SO(n). These manifolds are special cases of the compact, real Stiefel manifold St(p,n). Using tools from optimization and control theory, we prove that the generalized Kuramoto model on St(p,n) converges to a synchronized state for any connected graph and from almost all initial conditions provided (p,n) satisfies p≤2/3n−1 and all oscillator frequencies are equal. This result could not have been predicted based on knowledge of the Kuramoto model in complex networks over the circle. In that case, almost global synchronization is graph dependent; it applies if the network is acyclic or sufficiently dense. This paper hence identifies a property that distinguishes many high-dimensional generalizations of the Kuramoto models from the original model.
(Less)
- author
- Markdahl, Johan ; Thunberg, Johan LU and Goncalves, Jorge
- publishing date
- 2020-03
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Decentralization, Kuramoto model, Multi-agent system, Networked robotics, Stiefel manifold, Synchronization
- in
- Automatica
- volume
- 113
- article number
- 108736
- publisher
- Elsevier
- external identifiers
-
- scopus:85076454228
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2019.108736
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2019 Elsevier Ltd
- id
- 6af4667b-551f-4d17-aaf5-cc2aab46cb70
- date added to LUP
- 2024-09-05 12:28:14
- date last changed
- 2025-04-04 14:04:07
@article{6af4667b-551f-4d17-aaf5-cc2aab46cb70,
abstract = {{<p>The Kuramoto model of coupled phase oscillators is often used to describe synchronization phenomena in nature. Some applications, e.g., quantum synchronization and rigid-body attitude synchronization, involve high-dimensional Kuramoto models where each oscillator lives on the n-sphere or SO(n). These manifolds are special cases of the compact, real Stiefel manifold St(p,n). Using tools from optimization and control theory, we prove that the generalized Kuramoto model on St(p,n) converges to a synchronized state for any connected graph and from almost all initial conditions provided (p,n) satisfies p≤2/3n−1 and all oscillator frequencies are equal. This result could not have been predicted based on knowledge of the Kuramoto model in complex networks over the circle. In that case, almost global synchronization is graph dependent; it applies if the network is acyclic or sufficiently dense. This paper hence identifies a property that distinguishes many high-dimensional generalizations of the Kuramoto models from the original model.</p>}},
author = {{Markdahl, Johan and Thunberg, Johan and Goncalves, Jorge}},
issn = {{0005-1098}},
keywords = {{Decentralization; Kuramoto model; Multi-agent system; Networked robotics; Stiefel manifold; Synchronization}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Automatica}},
title = {{High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally}},
url = {{http://dx.doi.org/10.1016/j.automatica.2019.108736}},
doi = {{10.1016/j.automatica.2019.108736}},
volume = {{113}},
year = {{2020}},
}