Vol. 12, No. 6, 2019

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The number of fixed points of AND-OR networks with chain topology

Alan Veliz-Cuba and Lauren Geiser

Vol. 12 (2019), No. 6, 1051–1068
Abstract

AND-OR networks are Boolean networks where each coordinate function is either the AND or OR logical operator. We study the number of fixed points of these Boolean networks in the case that they have a wiring diagram with chain topology. We find closed formulas for subclasses of these networks and recursive formulas in the general case. Our results allow for an effective computation of the number of fixed points in the case that the topology of the Boolean network is an open chain (finite or infinite) or a closed chain. We further explore how our approach could be used in “fractal” chains.

Keywords
Boolean networks, steady states, fixed points, discrete-time systems, AND-OR networks
Mathematical Subject Classification 2010
Primary: 94C10, 06E30, 05C99
Milestones
Received: 3 January 2019
Accepted: 21 April 2019
Published: 3 August 2019

Communicated by Kenneth S. Berenhaut
Authors
Alan Veliz-Cuba
Department of Mathematics
University of Dayton
Dayton, OH
United States
Lauren Geiser
University of Dayton
Dayton, OH
United States