Attractors and transient in sequential dynamical systems. Issue 1 (1st February 2020)

• Record Type: Journal Article
• Authors: Aledo, Juan A.; Diaz, Luis G.; Martinez, Silvia; Valverde, Jose C.
• Is Part Of: International journal of computer mathematics. Volume 97:Issue 1/2(2020)
• Page Start: 467
• Page End: 481
• Publication Date: 2020-02-01
• Subjects: Sequential dynamical systems -- Boolean functions -- attractors -- basin of attraction -- global attractors -- transient; 90B10 -- 37E15 -- 68R10 -- 94C10; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2019.1647338
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this article, we show how to determine attractors in sequential dynamical systems on maxterm and minterm Boolean functions and their corresponding basins of attraction. Furthermore, we make possible to know when an attractor is globally attractive. As the main result of this work, upper bounds for the transient in such models are provided. In order to do that, we distinguish two possible scenarios: fixed point sequential dynamical systems and periodic orbit sequential dynamical systems.