Modular dynamical systems on networks
Lee DeVilleUniversity of Illinois at Urbana-Champaign, USA
Eugene LermanUniversity of Illinois at Urbana-Champaign, USA
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.
Cite this article
Lee DeVille, Eugene Lerman, Modular dynamical systems on networks. J. Eur. Math. Soc. 17 (2015), no. 12, pp. 2977–3013DOI 10.4171/JEMS/577