2007/12/06 by Piotr Fronczak, Agata Fronczak
Biochemistry, Genetics and Molecular Biology · Engineering · Physics and Astronomy · #Boolean model #Chaotic #Complex Network Analysis Techniques #Critical exponent #Critical line #Directed percolation #Gene Regulatory Network Analysis #Line (geometry) #Percolation (cognitive psychology) #Percolation threshold #Position (finance) #Randomness #Slime Mold and Myxomycetes Research #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/41/22/224009
published as J. Phys. A 41, 224009 (2008) · submitted to Journal of Physics A, special issue "Complex networks"
arxiv created 2007/12/06 · openalex publication_date 2008/05/21 · arxiv updated 2015/05/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that to describe correctly the position of the critical line in Kauffman random Boolean networks one must take into account percolation phenomena underlying the process of damage spreading. For this reason, since the issue of percolation transition is much simpler in random undirected networks than in the directed ones, we study the Kauffman model in undirected networks. We derive the mean field formula for the critical line in the giant components of these networks, and show that the critical line characterizing the whole network results from the fact that the ordered behavior of small clusters shields the chaotic behavior of the giant component. We also show a possible attitude towards the analytical description of the shielding effect. The theoretical derivations given in this paper very much tally with the numerical simulations done for classical random graphs.