2004/10/31 by Barbara Drossel, Tamara Mihaljev, Florian Greil · 5 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Bioinformatics and Genomic Networks #Gene Regulatory Network Analysis #Protein Structure and Dynamics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevlett.94.088701
published as Phys. Rev. Lett. 94, 088701 (2005) · 4 pages, no figure, no table; published in PRL
openalex publication_date 2005/03/04 · arxiv created 2005/03/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
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.