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Stabilization bounds for linear finite dynamical systems
Linnaeus University, Faculty of Technology, Department of Mathematics.
2018 (English)In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 511, p. 516-534Article in journal (Refereed) Published
Abstract [en]

A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the number of iterations needed for a system to settle on a fixed set of elements. As our main result, we present two upper bounds on iterations needed, and each one may be readily applied to a fixed point system test or a computation of limit cycles. The bounds are based on submodule properties of iterated images and reduced systems modulo a prime. We also provide examples where our bounds are optimal. (C) 2018 Elsevier Inc. All rights reserved.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 511, p. 516-534
Keywords [en]
Finite rings, Linear finite dynamical systems, Fixed point systems, Height
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-77488DOI: 10.1016/j.jalgebra.2018.04.009ISI: 000441495100028Scopus ID: 2-s2.0-85045314644OAI: oai:DiVA.org:lnu-77488DiVA, id: diva2:1244258
Available from: 2018-08-31 Created: 2018-08-31 Last updated: 2019-08-29Bibliographically approved

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