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Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs

Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain
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2010 Mathematics Subject Classification: Primary 90B10, Secondary 37E15, 94C10.
Mathematics 2020, 8(10), 1812; https://doi.org/10.3390/math8101812
Received: 13 August 2020 / Revised: 26 September 2020 / Accepted: 28 September 2020 / Published: 16 October 2020
(This article belongs to the Special Issue Boolean Networks Models in Science and Engineering)
In this work, we solve the problem of the coexistence of periodic orbits in homogeneous Boolean graph dynamical systems that are induced by a maxterm or a minterm (Boolean) function, with a direct underlying dependency graph. Specifically, we show that periodic orbits of any period can coexist in both kinds of update schedules, parallel and sequential. This result contrasts with the properties of their counterparts over undirected graphs with the same evolution operators, where fixed points cannot coexist with periodic orbits of other different periods. These results complete the study of the periodic structure of homogeneous Boolean graph dynamical systems on maxterm and minterm functions. View Full-Text
Keywords: Boolean networks; combinatorial dynamics; types of periodic orbits; Boolean algebra; Boolean functions Boolean networks; combinatorial dynamics; types of periodic orbits; Boolean algebra; Boolean functions
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Aledo, J.A.; Diaz, L.G.; Martinez, S.; Valverde, J.C. Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs. Mathematics 2020, 8, 1812.

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