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Network analysis of the state space of discrete dynamical systems.

Publication ,  Journal Article
Shreim, A; Grassberger, P; Nadler, W; Samuelsson, B; Socolar, JES; Paczuski, M
Published in: Physical review letters
May 2007

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.

Duke Scholars

Published In

Physical review letters

DOI

EISSN

1079-7114

ISSN

0031-9007

Publication Date

May 2007

Volume

98

Issue

19

Start / End Page

198701

Related Subject Headings

  • General Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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ICMJE
MLA
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Shreim, A., Grassberger, P., Nadler, W., Samuelsson, B., Socolar, J. E. S., & Paczuski, M. (2007). Network analysis of the state space of discrete dynamical systems. Physical Review Letters, 98(19), 198701. https://doi.org/10.1103/physrevlett.98.198701
Shreim, Amer, Peter Grassberger, Walter Nadler, Björn Samuelsson, Joshua E. S. Socolar, and Maya Paczuski. “Network analysis of the state space of discrete dynamical systems.Physical Review Letters 98, no. 19 (May 2007): 198701. https://doi.org/10.1103/physrevlett.98.198701.
Shreim A, Grassberger P, Nadler W, Samuelsson B, Socolar JES, Paczuski M. Network analysis of the state space of discrete dynamical systems. Physical review letters. 2007 May;98(19):198701.
Shreim, Amer, et al. “Network analysis of the state space of discrete dynamical systems.Physical Review Letters, vol. 98, no. 19, May 2007, p. 198701. Epmc, doi:10.1103/physrevlett.98.198701.
Shreim A, Grassberger P, Nadler W, Samuelsson B, Socolar JES, Paczuski M. Network analysis of the state space of discrete dynamical systems. Physical review letters. 2007 May;98(19):198701.

Published In

Physical review letters

DOI

EISSN

1079-7114

ISSN

0031-9007

Publication Date

May 2007

Volume

98

Issue

19

Start / End Page

198701

Related Subject Headings

  • General Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences