abstract

• We describe the transient regime of synchronizing flows defined over a network, 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.

authors

• Ugalde Saldaña Edgardo

publication date

• 2023-01-01

funding provided via

• Consejo Nacional de Ciencia y Tecnología (CONACyT) M16M01, 722957; Fundación Sofía Kovalevskaia; Sociedad Matemática Mexicana; Centre Nacional de la Recherche Scientifique (CNRS)  Grant

published in

• Journal of Physics A-Mathematical and Theoretical  Journal

keywords

• synchronization; Laplacian flow; Kuramoto model; complete graph; Dyck Paths; Polyminoes

Digital Object Identifier (DOI)

• 10.1088/1751-8121/acd03a

PubMed ID

start page

end page

volume

• 56

issue

• 22