Record 
Author 
Goles, E.; Lobos, F.; Ruz, G.A.; Sene, S. 
Title 
Attractor landscapes in Boolean networks with firing memory: a theoretical study applied to genetic networks 
Type 
Journal Article 
Year 
2020 
Publication 
Natural Computing 
Abbreviated Journal 
Nat. Comput. 
Volume 
to appear 
Issue 

Pages 
25 pp 
Keywords 
Discrete dynamical systems; Boolean networks; Biological network modeling 
Abstract 
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains at its firing state a finite number of steps. We prove in particular that these networks have the same computational power than the classical ones, i.e. any Boolean network with firing memory composed of m vertices can be simulated by a Boolean network by adding vertices. We also prove general results on specific classes of networks. For instance, we show that the existence of at least one delay greater than 1 in disjunctive networks makes such networks have only fixed points as attractors. Moreover, for arbitrary networks composed of two vertices, we characterize the delay phase space, i.e. the delay values such that networks admits limit cycles or fixed points. Finally, we analyze two classical biological models by introducing delays: the model of the immune control of the lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{69pt} \begin{document}$$\lambda $$\end{document}phage and that of the genetic control of the floral morphogenesis of the plant Arabidopsis thaliana. 
Address 
[Goles, Eric; Lobos, Fabiola; Ruz, Gonzalo A.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email: eric.chacc@uai.cl; 
Corporate Author 

Thesis 

Publisher 
Springer 
Place of Publication 

Editor 

Language 
English 
Summary Language 

Original Title 

Series Editor 

Series Title 

Abbreviated Series Title 

Series Volume 

Series Issue 

Edition 

ISSN 
15677818 
ISBN 

Medium 

Area 

Expedition 

Conference 

Notes 
WOS:000531210800001 
Approved 
no 
Call Number 
UAI @ eduardo.moreno @ 
Serial 
1139 
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