Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 11 (2015), 022, 21 pages      arXiv:1208.1513      https://doi.org/10.3842/SIGMA.2015.022

Dynamics on Networks of Manifolds

Lee DeVille and Eugene Lerman
Department of Mathematics, University of Illinois, USA

Received April 24, 2014, in final form February 24, 2015; Published online March 12, 2015

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.

Key words: coupled cell networks; open dynamical systems; control systems; morphisms of dynamical systems.

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