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...

Full description

Saved in:

Bibliographic Details
Published in:	Mathematics (Basel) Vol. 8; no. 10; p. 1812
Main Authors:	Aledo, Juan A., Diaz, Luis G., Martinez, Silvia, Valverde, Jose C.
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-10-2020
Subjects:	Algebra Boolean Boolean algebra Boolean functions Boolean networks combinatorial dynamics Dynamical systems Fixed points (mathematics) Graph theory Graphs Mathematics Operators (mathematics) Orbits Periodic structures Schedules types of periodic orbits
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	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.
ISSN:	2227-7390 2227-7390
DOI:	10.3390/math8101812