Cooperative Boolean systems with generically long attractors I

Abstract

We study the class of cooperative Boolean networks whose only regulatory functions are COPY, binary AND, and binary OR. We prove that for all sufficiently large N and c < 2 there exist Boolean networks in this class that have an attractor of length > c^N whose basin of attraction comprises an arbitrarily large fraction of the state space. The existence of such networks contrasts with results on various other types of dynamical systems that show nongenericity or absence of non-steady state attractors under the assumption of cooperativity.

arXiv commentThis is an Author's Original Manuscript of an article submitted for consideration in the Journal of Difference Equations and Applications [copyright Taylor & Francis]; Journal of Difference Equations and Applications is available online at http://www.tandfonline.com/doi/abs/10.1080/10236198.2012.691167

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• The effect of negative feedback loops on the dynamics of Boolean networks
• The properties of attractors of canalyzing random Boolean networks
• On the properties of cycles of simple Boolean networks
• Prevalent Behavior of Strongly Order Preserving Semiflows
• Extremely chaotic Boolean networks
• Cooperative Boolean systems with generically long attractors I

Cited by in corpus (1)

• Cooperative Boolean systems with generically long attractors I