Reference : Almost global convergence to practical synchronization in the generalized Kuramoto mo...
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
http://hdl.handle.net/10993/48041
Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere
English
Markdahl, Johan [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control >]
Proverbio, Daniele mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control >]
Mi, La [University of Luxembourg > Luxembourg Centre for Systems Biomedicine]
Goncalves, Jorge mailto [University of Luxembourg > Luxembourg Centre for Systems Biomedicine (LCSB) > Systems Control >]
20-Aug-2021
Communications Physics
Nature Publishing Group
4
Yes
2399-3650
United Kingdom
[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.
Fonds National de la Recherche - FnR
http://hdl.handle.net/10993/48041
10.1038/s42005-021-00689-y

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