On the properties of cycles of simple Boolean networks

Abstract

We study two types of simple Boolean networks, namely two loops with a cross-link and one loop with an additional internal link. Such networks occur as relevant components of critical K=2 Kauffman networks. We determine mostly analytically the numbers and lengths of cycles of these networks and find many of the features that have been observed in Kauffman networks. In particular, the mean number and length of cycles can diverge faster than any power law.

arXiv comment10 pages, 8 figures

References in corpus (4)

• Scaling in ordered and critical random Boolean networks
• Stability of the Kauffman Model
• Relevant elments, Magnetization and Dynamical Properties in Kauffman Networks: a Numerical Study
• The Modular Structure of Kauffman Networks

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• Cooperative Boolean systems with generically long attractors I
• Random logic networks: from classical Boolean to quantum dynamics