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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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Abstract
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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