On Fixed Point Convergence of Linear Finite Dynamical Systems

On Fixed Point Convergence of Linear Finite Dynamical Systems

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 n...

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Main Author: Lindenberg, Björn
Format: Others
Language:English
Published: Linnéuniversitetet, Institutionen för matematik (MA) 2016
Subjects:
finite dynamical systems
linear finite dynamical systems
fixed point systems
Online Access:http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-52891
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spelling ndltd-UPSALLA1-oai-DiVA.org-lnu-528912016-06-03T05:10:04ZOn Fixed Point Convergence of Linear Finite Dynamical SystemsengLindenberg, BjörnLinnéuniversitetet, Institutionen för matematik (MA)2016finite dynamical systemslinear finite dynamical systemsfixed point systemsA 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. Student thesisinfo:eu-repo/semantics/bachelorThesistexthttp://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-52891application/pdfinfo:eu-repo/semantics/openAccess
collection NDLTD
language English
format Others
sources NDLTD
topic finite dynamical systems
linear finite dynamical systems
fixed point systems
spellingShingle finite dynamical systems
linear finite dynamical systems
fixed point systems
Lindenberg, Björn
On Fixed Point Convergence of Linear Finite Dynamical Systems
description 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.
author Lindenberg, Björn
author_facet Lindenberg, Björn
author_sort Lindenberg, Björn
title On Fixed Point Convergence of Linear Finite Dynamical Systems
title_short On Fixed Point Convergence of Linear Finite Dynamical Systems
title_full On Fixed Point Convergence of Linear Finite Dynamical Systems
title_fullStr On Fixed Point Convergence of Linear Finite Dynamical Systems
title_full_unstemmed On Fixed Point Convergence of Linear Finite Dynamical Systems
title_sort on fixed point convergence of linear finite dynamical systems
publisher Linnéuniversitetet, Institutionen för matematik (MA)
publishDate 2016
url http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-52891
work_keys_str_mv AT lindenbergbjorn onfixedpointconvergenceoflinearfinitedynamicalsystems
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