Cooperative Boolean systems with generically long attractors II

2013/02/15 by Winfried Just, Just, Winfried, Maciej Malicki +1
Biochemistry, Genetics and Molecular Biology · Neuroscience · #34C12 #39A33 #94C10 #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Neural dynamics and brain function #Receptor Mechanisms and Signaling

paper · pdf · doi:10.48550/arxiv.1302.3830

openalex publication_date 2013/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that cooperativity in Boolean networks precludes a strong notion of sensitive dependence on initial conditions. Weaker notions of sensitive dependence are shown to be consistent with cooperativity, but if each regulatory functions is binary AND or binary OR, in N-dimensional networks they impose an upper bound of approximately sqrt(3)^N on the lengths of attractors that can be reached from a fraction p approaching 1 of initial conditions. The upper bound is shown to be sharp.

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