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

Juan A. Aledo, Luis G. Diaz, Silvia Martinez and Jose C. Valverde
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Juan A. Aledo: Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain
Luis G. Diaz: Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain
Silvia Martinez: Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain
Jose C. Valverde: Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, Spain

Mathematics, 2020, vol. 8, issue 10, 1-14

Abstract: 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.

Keywords: Boolean networks; combinatorial dynamics; types of periodic orbits; Boolean algebra; Boolean functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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