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Network analysis of the state space of discrete dynamical systems

Shreim, Amer; Grassberger, Peter; Nadler, Walter; Samuelsson, Björn LU ; Socolar, Joshua E. S. and Paczuski, Maya (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:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Letters
volume
98
issue
19
publisher
American Physical Society
external identifiers
  • scopus:34547367492
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
2008-10-31 09:03:20
date last changed
2017-05-28 03:30:01
@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.},
  articleno    = {198701},
  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},
  volume       = {98},
  year         = {2007},
}