Vol. 12, No. 6, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 4, 543–722
Issue 3, 363–541
Issue 2, 183–362
Issue 1, 1–182

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-4184 (online)
ISSN 1944-4176 (print)
 
Author index
To appear
 
Other MSP journals
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