Modular dynamical systems on networks

DeVille, Lee, and Lerman, Eugene. "Modular dynamical systems on networks." Journal of the European Mathematical Society 017.12 (2015): 2977-3013. <http://eudml.org/doc/277581>.

@article{DeVille2015,
abstract = {We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations, on the other hand, give rise to surjective maps from large dynamical systems to smaller ones. One can view these surjections as a kind of “fast/slow” variable decompositions or as “abstractions” in the computer science sense of the word.},
author = {DeVille, Lee, Lerman, Eugene},
journal = {Journal of the European Mathematical Society},
keywords = {dynamical systems; networks; modularity; graph fibrations; dynamical systems; networks; modularity; graph fibrations},
language = {eng},
number = {12},
pages = {2977-3013},
publisher = {European Mathematical Society Publishing House},
title = {Modular dynamical systems on networks},
url = {http://eudml.org/doc/277581},
volume = {017},
year = {2015},
}

TY - JOUR
AU - DeVille, Lee
AU - Lerman, Eugene
TI - Modular dynamical systems on networks
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 12
SP - 2977
EP - 3013
AB - We propose a new framework for the study of continuous time dynamical systems on networks. We view such dynamical systems as collections of interacting control systems. We show that a class of maps between graphs called graph fibrations give rise to maps between dynamical systems on networks. This allows us to produce conjugacy between dynamical systems out of combinatorial data. In particular we show that surjective graph fibrations lead to synchrony subspaces in networks. The injective graph fibrations, on the other hand, give rise to surjective maps from large dynamical systems to smaller ones. One can view these surjections as a kind of “fast/slow” variable decompositions or as “abstractions” in the computer science sense of the word.
LA - eng
KW - dynamical systems; networks; modularity; graph fibrations; dynamical systems; networks; modularity; graph fibrations
UR - http://eudml.org/doc/277581
ER -