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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 022, 21 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.022 (Mi sigma1003) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Dynamics on Networks of Manifolds

Lee Deville, Eugene Lerman

Department of Mathematics, University of Illinois, USA
Full-text PDF (472 kB) Citations (6)
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DOI: https://doi.org/10.3842/SIGMA.2015.022
Abstract: We propose a precise definition of a continuous time dynamical system made up of interacting open subsystems. The interconnections of subsystems are coded by directed graphs. We prove that the appropriate maps of graphs called graph fibrations give rise to maps of dynamical systems. Consequently surjective graph fibrations give rise to invariant subsystems and injective graph fibrations give rise to projections of dynamical systems.
Keywords: coupled cell networks; open dynamical systems; control systems; morphisms of dynamical systems.
Received: April 24, 2014; in final form February 24, 2015; Published online March 12, 2015
Bibliographic databases:
Document Type: Article
MSC: 34C14; 18D99
Language: English
Citation: Lee Deville, Eugene Lerman, “Dynamics on Networks of Manifolds”, SIGMA, 11 (2015), 022, 21 pp.
Citation in format AMSBIB
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\paper Dynamics on Networks of Manifolds
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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