Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2005-02-21
Physics
Condensed Matter
Statistical Mechanics
16 text pages, 13 figures. To be published in Physica A
Scientific paper
10.1016/j.physa.2005.02.019
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent rules, each containing a single parameter. We observe that changes in graph topology induce transitions between different dynamic domains (Wolfram classes) without a formal change in the update rule. Along with topological variations, we study the pattern formation capacities of regular, random, small-world and scale-free graphs. Pattern formation capacity is quantified in terms of two entropy measures, which for standard cellular automata allow a qualitative distinction between the four Wolfram classes. A mean-field model explains the dynamic behavior of random graphs. Implications for our understanding of information transport through complex, network-based systems are discussed.
Huett Marc-Thorsten
Marr Carsten
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