Geodesic
Modular dynamical systems on networks
Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 2977-3013 Cet article a éte moissonné depuis la source EMS Press

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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.
DOI : 10.4171/jems/577
Classification : 37-XX, 18-XX
Keywords: Dynamical systems, networks, modularity, graph fibrations 
@article{JEMS_2015_17_12_a0,
     author = {Lee DeVille and Eugene Lerman},
     title = {Modular dynamical systems on networks},
     journal = {Journal of the European Mathematical Society},
     pages = {2977--3013},
     year = {2015},
     volume = {17},
     number = {12},
     doi = {10.4171/jems/577},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/577/}
}
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Lee DeVille; Eugene Lerman. Modular dynamical systems on networks. Journal of the European Mathematical Society, Tome 17 (2015) no. 12, pp. 2977-3013. doi: 10.4171/jems/577

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