Network analysis of the state space of discrete dynamical systems.

Journal Article (Journal Article)

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.

Full Text

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Duke Authors

Socolar, Joshua

Cited Authors

Shreim, A; Grassberger, P; Nadler, W; Samuelsson, B; Socolar, JES; Paczuski, M

Published Date

May 2007

Published In

Physical Review Letters

Volume / Issue

98 / 19

Start / End Page

198701 -

PubMed ID

17677672

Electronic International Standard Serial Number (EISSN)

1079-7114

International Standard Serial Number (ISSN)

0031-9007

Digital Object Identifier (DOI)

10.1103/physrevlett.98.198701

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