2001/07/02 by Sven Bilke, S. Bilke, Fredrik Sjunnesson +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Neuroscience · Physics and Astronomy · #Gene Regulatory Network Analysis #Neural dynamics and brain function #Nonlinear Dynamics and Pattern Formation #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.65.016129
12 pages, 4 figures
arxiv created 2001/07/02 · openalex publication_date 2001/12/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Random Boolean networks, the Kauffman model, are revisited by means of a novel decimation algorithm, which removes variables that cannot be relevant to the asymptotic dynamics of the system. The major part of the removed variables have the same fixed state in all limit cycles. These variables are denoted as the stable core of the network and their number grows approximately linearly with N, the number of variables in the original network. The sensitivity of the attractors to perturbations is investigated. We find that reduced networks lack the well-known insensitivity observed in full Kauffman networks. We conclude that, somewhat counterintuitive, this remarkable property of full Kauffman networks is generated by the dynamics of their stable core. The decimation method is also used to simulate large critical Kauffman networks. For networks up to N=32 we perform full enumeration studies. Strong evidence is provided that the number of limit cycles grows linearly with N. This result is in sharp contrast to the often cited square root of [N] behavior.