Publication :
Spectral dimension reduction of complex dynamical networks

En cours de chargement...
Vignette d'image
Date
2019-03-04
Direction de publication
Direction de recherche
Titre de la revue
ISSN de la revue
Titre du volume
Éditeur
American Physical Society
Projets de recherche
Structures organisationnelles
Numéro de revue
Résumé
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve (nodes’ dynamics). Despite substantial progress, little is known about why some subtle changes in the network structure, at the so-called critical points, can provoke drastic shifts in its dynamics. We tackle this challenging problem by introducing a method that reduces any network to a simplified low-dimensional version. It can then be used to describe the collective dynamics of the original system. This dimension reduction method relies on spectral graph theory and, more specifically, on the dominant eigenvalues and eigenvectors of the network adjacency matrix. Contrary to previous approaches, our method is able to predict the multiple activation of modular networks as well as the critical points of random networks with arbitrary degree distributions. Our results are of both fundamental and practical interest, as they offer a novel framework to relate the structure of networks to their dynamics and to study the resilience of complex systems.
Description
Revue
Physical review x, Vol. 9 (1) (2019)
DOI
10.1103/PhysRevX.9.011042
URL vers la version publiée
Mots-clés
Complex Systems , Nonlinear Dynamics , Statistical Physics
Citation
Type de document
article de recherche