Counting Periodic Points in Parallel Graph Dynamical Systems
Joint Authors
Barzanouni, Ali
Aledo, J.
Valverde, Jose C.
Malekbala, Ghazaleh
Sharifan, Leila
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-14
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
Let F:0,1n⟶0,1n be a parallel dynamical system over an undirected graph with a Boolean maxterm or minterm function as a global evolution operator.
It is well known that every periodic point has at most two periods.
Actually, periodic points of different periods cannot coexist, and a fixed point theorem is also known.
In addition, an upper bound for the number of periodic points of F has been given.
In this paper, we complete the study, solving the minimum number of periodic points’ problem for this kind of dynamical systems which has been usually considered from the point of view of complexity.
In order to do this, we use methods based on the notions of minimal dominating sets and maximal independent sets in graphs, respectively.
More specifically, we find a lower bound for the number of fixed points and a lower bound for the number of 2-periodic points of F.
In addition, we provide a formula that allows us to calculate the exact number of fixed points.
Furthermore, we provide some conditions under which these lower bounds are attained, thus generalizing the fixed-point theorem and the 2-period theorem for these systems.
American Psychological Association (APA)
Aledo, J.& Barzanouni, Ali& Malekbala, Ghazaleh& Sharifan, Leila& Valverde, Jose C.. 2020. Counting Periodic Points in Parallel Graph Dynamical Systems. Complexity،Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1145773
Modern Language Association (MLA)
Aledo, J.…[et al.]. Counting Periodic Points in Parallel Graph Dynamical Systems. Complexity No. 2020 (2020), pp.1-9.
https://search.emarefa.net/detail/BIM-1145773
American Medical Association (AMA)
Aledo, J.& Barzanouni, Ali& Malekbala, Ghazaleh& Sharifan, Leila& Valverde, Jose C.. Counting Periodic Points in Parallel Graph Dynamical Systems. Complexity. 2020. Vol. 2020, no. 2020, pp.1-9.
https://search.emarefa.net/detail/BIM-1145773
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1145773