On Fixed Point Convergence of Linear Finite Dynamical Systems
Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
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.
finite dynamical systems, linear finite dynamical systems, fixed point systems
IdentifiersURN: urn:nbn:se:lnu:diva-52891OAI: oai:DiVA.org:lnu-52891DiVA: diva2:932546
Subject / course
Applied Mahtematics Programme, 180 credits
Svensson, Per-Anders, Universitetslektor
Lindahl, Karl-Olof, Docent