Dr Maximilien Gadouleau m.r.gadouleau@durham.ac.uk
Associate Professor
Simple dynamics on graphs
Gadouleau, Maximilien; Richard, Adrien
Authors
Adrien Richard
Abstract
Can the interaction graph of a finite dynamical system force this system to have a “complex” dynamics? In other words, given a finite interval of integers A, which are the signed digraphs G such that every finite dynamical system f:An→An with G as interaction graph has a “complex” dynamics? If |A|≥3 we prove that no such signed digraph exists. More precisely, we prove that for every signed digraph G there exists a system f:An→An with G as interaction graph that converges toward a unique fixed point in at most ⌊log2n⌋+2 steps. The boolean case |A|=2 is more difficult, and we provide partial answers instead. We exhibit large classes of unsigned digraphs which admit boolean dynamical systems which converge toward a unique fixed point in polynomial, linear or constant time.
Citation
Gadouleau, M., & Richard, A. (2016). Simple dynamics on graphs. Theoretical Computer Science, 628, 62-77. https://doi.org/10.1016/j.tcs.2016.03.013
Journal Article Type | Article |
---|---|
Acceptance Date | Mar 8, 2016 |
Online Publication Date | Mar 10, 2016 |
Publication Date | Mar 10, 2016 |
Deposit Date | Aug 26, 2016 |
Publicly Available Date | Mar 28, 2024 |
Journal | Theoretical Computer Science |
Print ISSN | 0304-3975 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 628 |
Pages | 62-77 |
DOI | https://doi.org/10.1016/j.tcs.2016.03.013 |
Files
Accepted Journal Article
(354 Kb)
PDF
Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
You might also like
Bent functions in the partial spread class generated by linear recurring sequences
(2022)
Journal Article
Expansive automata networks
(2020)
Journal Article
Fixing monotone Boolean networks asynchronously
(2020)
Journal Article
Elementary, finite and linear vN-regular cellular automata
(2020)
Journal Article
Complete Simulation of Automata Networks
(2019)
Journal Article
Downloadable Citations
About Durham Research Online (DRO)
Administrator e-mail: dro.admin@durham.ac.uk
This application uses the following open-source libraries:
SheetJS Community Edition
Apache License Version 2.0 (http://www.apache.org/licenses/)
PDF.js
Apache License Version 2.0 (http://www.apache.org/licenses/)
Font Awesome
SIL OFL 1.1 (http://scripts.sil.org/OFL)
MIT License (http://opensource.org/licenses/mit-license.html)
CC BY 3.0 ( http://creativecommons.org/licenses/by/3.0/)
Powered by Worktribe © 2024
Advanced Search