# Modular dynamical systems on networks

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 12, page 2977-3013
- ISSN: 1435-9855

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topDeVille, 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 -

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