Paths towards synchronization: analytical treatment of completely connected networks
Résumé
We describe the transient regime of synchronizing flows defined over a net-
work, introducing a codification of the paths towards synchronization. In all
cases, the collection of paths toward synchronization defines a combinatorial
structure: the transition diagram. In this paper, besides introducing this general
framework, we study in full detail the case of completely connected networks
where a monotonic convergence towards synchronization takes place. For
these systems we are able to supply a detailed analytical description of the
transition diagram describing both, the Laplacian flow and a special case of
the Kuramoto model on the same network. This constitutes a first instance of
a full symbolic description of the path towards synchronization and illustrates
the hidden complexity of the transient regime.
Domaines
Systèmes dynamiques [math.DS]
Origine : Fichiers produits par l'(les) auteur(s)