2008/08/22 by Tiago P. Peixoto, Barbara Drossel
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Algorithm #Bioinformatics and Genomic Networks #Boolean function #Boolean network #Combinatorics #Computer science #Discrete mathematics #Distribution (mathematics) #Function (biology) #Gene Regulatory Network Analysis #Hamming code #Hamming distance #Mathematical analysis #Mathematics #Node (physics) #Noise (video) #Order (exchange) #Physics #Quantum mechanics #Statistical physics #cond-mat.dis-nn #physics.bio-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1103/physreve.79.036108
9 pages, 8 figures, 1 table
arxiv created 2008/08/22 · openalex publication_date 2009/03/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate the effect of noise on random Boolean networks. Noise is implemented as a probability p that a node does not obey its deterministic update rule. We define two order parameters, the long-time average of the Hamming distance between a network with and without noise, and the average frozenness, which is a measure of the extent to which a node prefers one of the two Boolean states. We evaluate both order parameters as function of the noise strength, and of the number of inputs per node K finding a smooth transition from deterministic (p=0) to fully stochastic (p=12) dynamics for networks with K < or = 2 , and a first-order transition at p=0 for K>2 . Most of the results obtained by computer simulation are also derived analytically. The average Hamming distance can be evaluated using the annealed approximation. In order to obtain the distribution of frozenness as function of the noise strength, more sophisticated self-consistent calculations had to be performed. This distribution is a collection of delta peaks for K=1 , and it has a fractal sructure for K>1 , approaching a continuous distribution in the limit K1 .