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Modular dynamical systems on networks
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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.
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Cited by 2 Pith papers
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Networks of hybrid open systems
Hybrid open systems, their networks, and maps between networks are defined categorically, and maps between networks are shown to induce maps between the interconnected hybrid systems.
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Runge-Kutta and Networks
Runge-Kutta discretization commutes with every affine map that relates two vector fields, so affine invariant submanifolds such as synchrony polydiagonals are preserved in the discrete dynamics.
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