High-dimensional Kuramoto models on Stiefel manifolds synchronize complex networks almost globally
2020 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 113, article id 108736Article in journal (Refereed) Published
Abstract [en]
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. © 2019 Elsevier Ltd
Place, publisher, year, edition, pages
Amsterdam: Elsevier, 2020. Vol. 113, article id 108736
Keywords [en]
Decentralization, Kuramoto model, Multi-agent system, Networked robotics, Stiefel manifold, Synchronization, Complex networks, Graph theory, Multi agent systems, Coupled phase oscillators, Global synchronization, Kuramoto models, Optimization and control, Real stiefel manifold
National Category
Computational Mathematics Control Engineering
Identifiers
URN: urn:nbn:se:hh:diva-41484DOI: 10.1016/j.automatica.2019.108736ISI: 000514216600001Scopus ID: 2-s2.0-85076454228OAI: oai:DiVA.org:hh-41484DiVA, id: diva2:1390730
2020-02-032020-02-032021-10-25Bibliographically approved