Polyhedral Dynamics and the Geometry of Systems

Atkin, R. & Casti, J.L. (1977). Polyhedral Dynamics and the Geometry of Systems. IIASA Research Report. IIASA, Laxenburg, Austria: RR-77-006

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Using elementary concepts from algebraic topology, a program is outlined for the application of topological notions to the problem of characterizing the connective structure of large-scale systems. The basic approach is to generate appropriate mappings which associate a given system with a simplicial complex. Topological tools are then used in a non-standard manner to investigate the connectivity pattern of the system. Auxiliary notions such as eccentricity of a simplex, patterns on a complex, and the homological structure of a complex are also shown to have system- theoretic relevance.

The general ideas of the paper are illustrated on a number of simple examples, including the standard linear system set-up. The paper concludes with a discussion of several research topics to be carried out in an attempt to connect the algebraic-topological ideas with other branches of mathematical system theory.

Item Type: Monograph (IIASA Research Report)
Research Programs: System and Decision Sciences - Core (SDS)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 01:44
Last Modified: 27 Aug 2021 17:08
URI: https://pure.iiasa.ac.at/709

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