Geodesic
Dynamics on Networks of Manifolds
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{SIGMA_2015_11_a21,
     author = {Lee Deville and Eugene Lerman},
     title = {Dynamics on {Networks} of {Manifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2015},
     volume = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a21/}
}
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Lee Deville; Eugene Lerman. Dynamics on Networks of Manifolds. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a21/

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