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Generative network automata

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Hiroki Sayama, Department of Bioengineering, Binghamton University
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A variety of modeling frameworks have been proposed and
utilized in complex systems studies, including dynamical systems models that
describe state transitions within a system of fixed topology, and complex
networks models that describe topological transformations of a network with
little attention paid to dynamical state changes. However, many real-world
complex systems exhibit both of these two dynamics simultaneously. Here we
propose a novel modeling framework, "Generative Network Automata (GNA)",
that can uniformly describe both state transitions and autonomous topology
transformations of complex dynamical systems. The evolution of GNA is
defined as a generative process realized by repetitive local subnetwork
rewritings. We will present the formal definition of GNA, its generality to
represent other dynamical systems models, and some preliminary results of an
exhaustive sweep of possible dynamics found in elementary binary GNA with
restricted updating rules.