The Kuramoto model on oriented and signed graphs

Dörfler, Florian (Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH) Zürich, Switzerland) ; Delabays, Robin (Automatic Control Laboratory, Swiss Federal Institute of Technology (ETH) Zürich, Switzerland ; School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland) ; Jacquod, Philippe (School of Engineering, HES-SO Valais-Wallis, HEI, HES-SO // University of Applied Sciences Western Switzerland)

Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have an identical amplitude and/or sign. To describe synchronization phenomena in such systems, we use a generalized Kuramoto model with oriented, weighted, and signed interactions. Taking a bottom-up approach, we investigate the simplest possible oriented networks, namely, acyclic oriented networks and oriented cycles. These two types of networks are fundamental building blocks from which many general oriented networks can be constructed. For acyclic, weighted, and signed networks, we are able to completely characterize synchronization properties through necessary and sufficient conditions, which we show are optimal. Additionally, we prove that if it exists, a stable synchronous state is unique. In oriented, weighted, and signed cycles with identical natural frequencies, we show that the system globally synchronizes and that the number of stable synchronous states is finite.


Keywords:
Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEI-VS
Institute:
Institut Énergie et environnement
Date:
2019-02
Pagination:
23 p.
Published in:
SIAM Journal on Applied Dynamical Systems
Numeration (vol. no.):
2019, vol. 18, no.1 pp. 458-480
DOI:
ISSN:
1536-0040
Appears in Collection:



 Record created 2020-01-24, last modified 2020-01-24

Fulltext:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)