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

Veliz-Cuba, Alan; Geiser, Lauren

doi:10.2140/involve.2019.12.1051

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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

DOI: 10.2140/involve.2019.12.1051

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

Vol. 12, No. 6, 2019