Spectral Analysis of Attractors in Random Boolean Network Models

Circuits and loops in graph systems can be used to model the attractors in gene-regulatory networks. The number of such attractors grows very rapidly with network size and even for small nets the properties of the set of attractors, including their length distribution, are not well understood. This paper presents a Fourier spectral analysis of attractor lengths in a set of networks using Kauffman's NK random boolean network model. This allows a systematic study of the bulkaverage properties of the attractor distribution for different network connectivities without resorting to computationally expensive exact enumeration techniques. Networks with nodes of fixed degree and with distributions of different degree are studied. The length distribution of attractors flattens out above a connectivity of K = 2. It is hypothesised that discontinuities in the distribution are due to partial unreachability that arise even in single component nets at low connectivities.

• Type: Journal
• Year: 2009
• Where: FCS
• Authors: Kenneth A. Hawick
• Keywords: Computer Science, Expensive Exact Enumeration, FCS 2009, Fourier Spectral Analysis, Length Distribution