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[2105.12282] Operadic Modeling of Dynamical Systems: Mathematics and Computation

arxiv.org · 6,107 words · saved by 1 readers

Dynamical systems are ubiquitous in science and engineering as models of phenomena that evolve over time. Although complex dynamical systems tend to have important modular structure, conventional modeling approaches suppress this structure. Building on recent work in applied category theory, we show how deterministic dynamical systems, discrete and continuous, can be composed in a hierarchical style. In mathematical terms, we reformulate some existing operads of wiring diagrams and introduce new ones, using the general formalism of $\mathcal{C}$-sets (copresheaves). We then establish dynamical systems as algebras of these operads. In a computational vein, we show that Euler's method is functorial for undirected systems, extending a previous result for directed systems. All the ideas in this paper are implemented as practical software using Catlab and the AlgebraicJulia ecosystem, written in the Julia programming language for scientific computing.

Operadic Modeling of Dynamical Systems: Mathematics and Computation Sophie Libkind Andrew Baas Stanford University Georgia Tech Research Institute Palo Alto, California, USA Atlanta, Georgia, USA slibkind@stanford.edu andrew.baas@gtri.gatech.edu Evan Patterson James Fairbanks Topos Institute University of Florida…

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