2012/06/13 by Winfried Just, Maciej Malicki
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Arithmetic #Attractor #Binary number #Boolean function #Boolean network #Cellular Automata and Applications #Class (philosophy) #Combinatorics #Computer science #Discrete mathematics #Dynamical systems theory #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical analysis #Mathematics #Pure mathematics #State (computer science) #State space #math.DS #msc:34C12 #msc:39A33 #msc:94C10
paper · pdf · doi:10.1080/10236198.2012.691167
This 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
openalex publication_date 2012/06/13 · arxiv created 2013/02/13 · arxiv updated 2013/02/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 sharply contrasts with results on continuous dynamical systems that imply non-genericity of non-steady-state attractors under the assumption of cooperativity.