Article (Scientific journals)
Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere
Markdahl, Johan; Proverbio, Daniele; Mi, La et al.
2021In Communications Physics, 4
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Abstract :
[en] From the flashing of fireflies to autonomous robot swarms, synchronization phenomena are ubiquitous in nature and technology. They are commonly described by the Kuramoto model that, in this paper, we generalise to networks over n-dimensional spheres. We show that, for almost all initial conditions, the sphere model converges to a set with small diameter if the model parameters satisfy a given bound. Moreover, for even n, a special case of the generalized model can achieve phase synchronization with nonidentical frequency parameters. These results contrast with the standard n = 1 Kuramoto model, which is multistable (i.e., has multiple equilibria), and converges to phase synchronization only if the frequency parameters are identical. Hence, this paper shows that the generalized network Kuramoto models for n ≥ 2 displays more coherent and predictable behavior than the standard n = 1 model, a desirable property both in flocks of animals and for robot control.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Markdahl, Johan ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control
Proverbio, Daniele ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control
Mi, La;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine
Goncalves, Jorge ;  University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control
External co-authors :
yes
Language :
English
Title :
Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere
Publication date :
20 August 2021
Journal title :
Communications Physics
ISSN :
2399-3650
Publisher :
Nature Publishing Group, United Kingdom
Volume :
4
Peer reviewed :
Peer Reviewed verified by ORBi
Funders :
FNR - Fonds National de la Recherche [LU]
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