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On Fixed Point Convergence of Linear Finite Dynamical Systems
Linnaeus University, Faculty of Technology, Department of Mathematics.
2016 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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, and if every element eventually converges on fixed points. 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. The bounds are based on submodule properties of iterated images and reduced systems modulo a prime.

Place, publisher, year, edition, pages
2016. , 38 p.
Keyword [en]
finite dynamical systems, linear finite dynamical systems, fixed point systems
National Category
URN: urn:nbn:se:lnu:diva-52891OAI: diva2:932546
Subject / course
Educational program
Applied Mahtematics Programme, 180 credits
Available from: 2016-06-02 Created: 2016-06-01 Last updated: 2016-06-02Bibliographically approved

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fulltext(2315 kB)37 downloads
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Type fulltextMimetype application/pdf

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Lindenberg, Björn
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Department of Mathematics

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