Network Analysis of the State Space of Discrete Dynamical Systems
统计力学
2009-11-11 v3 元胞自动机与格子气
摘要
We study networks representing the dynamics of elementary 1-d 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 \emph{path diversity} as a global network measure. The co-appearance of non-trivial scaling in both hub size and path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's Class IV and some Class III CA.
引用
@article{arxiv.cond-mat/0610447,
title = {Network Analysis of the State Space of Discrete Dynamical Systems},
author = {Amer Shreim and Peter Grassberger and Walter Nadler and Björn Samuelsson and Joshua E. S. Socolar and Maya Paczuski},
journal= {arXiv preprint arXiv:cond-mat/0610447},
year = {2009}
}
备注
major revision; includes also improved numerics