Network analysis of the state space of discrete dynamical systems
(2007) In Physical Review Letters 98(19).- Abstract
- We study networks representing the dynamics of elementary 1D cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54, and 110. We further define the path diversity as a global network measure. The coappearance of nontrivial scaling in both the hub size and the path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram’s class IV and some class III CA.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1260853
- author
- Shreim, Amer ; Grassberger, Peter ; Nadler, Walter ; Samuelsson, Björn LU ; Socolar, Joshua E. S. and Paczuski, Maya
- publishing date
- 2007
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Physical Review Letters
- volume
- 98
- issue
- 19
- article number
- 198701
- publisher
- American Physical Society
- external identifiers
-
- scopus:34547367492
- pmid:17677672
- ISSN
- 1079-7114
- DOI
- 10.1103/PhysRevLett.98.198701
- language
- English
- LU publication?
- no
- id
- 9b10fcbc-382d-4216-880d-c21a55bff8a2 (old id 1260853)
- alternative location
- http://link.aps.org/abstract/PRL/v98/e198701
- date added to LUP
- 2016-04-01 11:38:42
- date last changed
- 2022-01-26 08:05:34
@article{9b10fcbc-382d-4216-880d-c21a55bff8a2, abstract = {{We study networks representing the dynamics of elementary 1D cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54, and 110. We further define the path diversity as a global network measure. The coappearance of nontrivial scaling in both the hub size and the path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram’s class IV and some class III CA.}}, author = {{Shreim, Amer and Grassberger, Peter and Nadler, Walter and Samuelsson, Björn and Socolar, Joshua E. S. and Paczuski, Maya}}, issn = {{1079-7114}}, language = {{eng}}, number = {{19}}, publisher = {{American Physical Society}}, series = {{Physical Review Letters}}, title = {{Network analysis of the state space of discrete dynamical systems}}, url = {{http://dx.doi.org/10.1103/PhysRevLett.98.198701}}, doi = {{10.1103/PhysRevLett.98.198701}}, volume = {{98}}, year = {{2007}}, }