Modular dynamical systems on networks

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)2977-3013
Number of pages37
JournalJournal of the European Mathematical Society
Volume17
Issue number12
DOIs
StatePublished - Jan 1 2015

Keywords

  • Dynamical systems
  • Graph fibrations
  • Modularity
  • Networks

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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