Global topological synchronization on simplicial and cell complexes
Statistical Mechanics
2023-05-17 v2 Mathematical Physics
Dynamical Systems
math.MP
Adaptation and Self-Organizing Systems
Physics and Society
Abstract
Topological signals, i.e., dynamical variables defined on nodes, links, triangles, etc. of higher-order networks, are attracting increasing attention. However the investigation of their collective phenomena is only at its infancy. Here we combine topology and nonlinear dynamics to determine the conditions for global synchronization of topological signals defined on simplicial or cell complexes. On simplicial complexes we show that topological obstruction impedes odd dimensional signals to globally synchronize. On the other hand, we show that cell complexes can overcome topological obstruction and in some structures, signals of any dimension can achieve global synchronization.
Cite
@article{arxiv.2208.14783,
title = {Global topological synchronization on simplicial and cell complexes},
author = {Timoteo Carletti and Lorenzo Giambagli and Ginestra Bianconi},
journal= {arXiv preprint arXiv:2208.14783},
year = {2023}
}