Counting attractors in synchronously updated random Boolean networks

Details Counting attractors in synchronously updated random Boolean networks Counting attractors in synchronously updated random Boolean networks

2004-12-16

arxiv.org/abs/q-bio/0412035v1

Biology

Quantitative Biology

Molecular Networks

11 pages, 6 figures

Scientific paper

Despite their apparent simplicity, random Boolean networks display a rich variety of dynamical behaviors. Much work has been focused on the properties and abundance of attractors. We here derive an expression for the number of attractors in the special case of one input per node. Approximating some other non-chaotic networks to be of this class, we apply the analytic results to them. For this approximation, we observe a strikingly good agreement on the numbers of attractors of various lengths. Furthermore, we find that for long cycle lengths, there are some properties that seem strange in comparison to real dynamical systems. However, those properties can be interesting from the viewpoint of constraint satisfaction problems.

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