- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:11
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
17
2015
12
Modular dynamical systems on networks
Lee
DeVille
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Eugene
Lerman
University of Illinois at Urbana-Champaign, URBANA, UNITED STATES
Dynamical systems, networks, modularity, graph fibrations
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.
Dynamical systems and ergodic theory
Category theory; homological algebra
2977
3013
10.4171/JEMS/577
http://www.ems-ph.org/doi/10.4171/JEMS/577