Number and length of attractors in a critical Kauffman model with connectivity one

Details Number and length of attractors in a critical Kauffman model with connectivity one Number and length of attractors in a critical Kauffman model with connectivity one

2004-10-22

arxiv.org/abs/cond-mat/0410579v2

Phys. Rev. Lett. 94, 088701 (2005)

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, no figure, no table; published in PRL

Scientific paper

10.1103/PhysRevLett.94.088701

The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.

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