@inproceedings{Macauley2009CycleEO,
title={Cycle equivalence of graph dynamical systems},
author={Matthew Macauley and Henning S. Mortveit},
year={2009}
}

Graph dynamical systems (GDSs) generalize concepts such as cellular automata and Boolean networks and can describe a wide range of distributed, nonlinear phenomena. Two GDSs are cycle equivalent if their periodic orbits are isomorphic as directed graphs, which captures the notion of having comparable long-term dynamics. In this paper, we study cycle equivalence of GDSs in which the vertex functions are applied sequentially through an update sequence. The main result is a general… CONTINUE READING

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