2002/09/25 by Maximino Aldana, Aldana, Maximino
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Gene Regulatory Network Analysis #Slime Mold and Myxomycetes Research #Statistical Mechanics (cond-mat.stat-mech) #Topological and Geometric Data Analysis #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0209571
4 pages, 3 figures
arxiv created 2002/09/25 · openalex publication_date 2002/09/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of Boolean networks (the N-K model) with scale-free topology are studied here. The existence of a phase transition governed by the value of the scale-free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories. The phase diagram shows that the phase transition occurs for values of the scale-free exponent in the open interval (2,2.5). Since the Boolean networks under study are directed graphs, the scale-free topology of the input connections and that of the output connections are studied separately. Ultimately these two topologies are shown to be equivalent. An important result of this work is that the fine-tuning usually required to achieve stability in Boolean networks with a totally random topology is no longer necessary when the network topology is scale-free.