Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs
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 bo...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1812 |
| _version_ | 1827704108041109504 |
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| author | Juan A. Aledo Luis G. Diaz Silvia Martinez Jose C. Valverde |
| author_facet | Juan A. Aledo Luis G. Diaz Silvia Martinez Jose C. Valverde |
| author_sort | Juan A. Aledo |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T15:33:05Z |
| format | Article |
| id | doaj.art-00a1c1a84f634fdcbde027c9e77e4eb1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:33:05Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-00a1c1a84f634fdcbde027c9e77e4eb12023-11-20T17:24:13ZengMDPI AGMathematics2227-73902020-10-01810181210.3390/math8101812Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed GraphsJuan A. Aledo0Luis G. Diaz1Silvia Martinez2Jose C. Valverde3Department of Mathematics, University of Castilla-La Mancha, 02071 Albacete, SpainDepartment of Mathematics, University of Castilla-La Mancha, 02071 Albacete, SpainDepartment of Mathematics, University of Castilla-La Mancha, 02071 Albacete, SpainDepartment of Mathematics, University of Castilla-La Mancha, 02071 Albacete, SpainIn 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.https://www.mdpi.com/2227-7390/8/10/1812Boolean networkscombinatorial dynamicstypes of periodic orbitsBoolean algebraBoolean functions |
| spellingShingle | Juan A. Aledo Luis G. Diaz Silvia Martinez Jose C. Valverde Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs Mathematics Boolean networks combinatorial dynamics types of periodic orbits Boolean algebra Boolean functions |
| title | Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs |
| title_full | Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs |
| title_fullStr | Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs |
| title_full_unstemmed | Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs |
| title_short | Coexistence of Periods in Parallel and Sequential Boolean Graph Dynamical Systems over Directed Graphs |
| title_sort | coexistence of periods in parallel and sequential boolean graph dynamical systems over directed graphs |
| topic | Boolean networks combinatorial dynamics types of periodic orbits Boolean algebra Boolean functions |
| url | https://www.mdpi.com/2227-7390/8/10/1812 |
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