 Dynamical attraction in parallel network modelsJuan A. Aledo, Luis G. Diaz, Silvia Martinez and Jose C. Valverde Applied Mathematics and Computation, 2019, vol. 361, issue C, 874-888 Abstract: In this work, we give a characterization of attractors in parallel deterministic network models, which evolve by means of maxterm and minterm Boolean functions and provide a method to obtain their basins of attraction. In order to do that, we distinguish the two possible cases: attractive fixed points and attractive 2-periodic orbits. Furthermore, we state necessary and sufficient conditions to know when a fixed point or a 2-periodic orbit is globally attractive. This makes possible to obtain a detailed description of their phase diagrams. Besides, we provide optimal upper bounds for the transient in such models, i.e., for the maximum number of iterations required to reach one of the periodic orbits. Moreover, we establish patterns that allow us to obtain a PDS on a maxterm or minterm Boolean function for which any given optimal upper bound for the transient is reached. Keywords: Deterministic network models; Boolean algebra; Boolean functions; Reachability; Attractors; Basin of attraction; Transient (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:874-888 DOI: 10.1016/j.amc.2019.05.048 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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