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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Physics A: Mathematical and Theoretical
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
