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ALGEBRAIC STRUCTURES ON A SET OF DISCRETE DYNAMICAL SYSTEM AND A SET OF PROFILE

BAREKENG: Jurnal Ilmu Matematika dan Terapan · Vol. 18 No. 1 (2024) · pp. 0065–0074

DOI
10.30598/barekengvol18iss1pp0065-0074
ISSN
2615-3017, 1978-7227
Published
2024-03-01
Publisher
PATTIMURA UNIVERSITY
Language
eng
License
creativecommons.org/licenses/by-sa/4.0

Abstract

A discrete dynamical system is represented as a directed graph with graph nodes called states that can be seen on the dynamical map. This discrete dynamical system is symbolized by, where is a finite set of states and the function g is a function from to. In the dynamical map, the discrete dynamical system has a height where the number of states in each height is called a profile. The set of discrete dynamical systems has an addition operation defined as a disjoint union on the graph and a multiplication operation defined as a tensor product on the graph. The set of discrete dynamical systems and the set of profiles are very interesting to observe from the algebraic point of view. Considering operation on the set of discrete dynamical systems and the set of profiles, we can see their algebraic structure. By recognizing the algebraic structure, it will be easy to solve the polynomial equation in the discrete dynamical system and in the profile. In this research, we will investigate the algebraic structure of discrete dynamical systems and the set of profiles. This research shows that the set of discrete dynamical system has an algebraic structure, which is a commutative semiring and the set of profiles has an algebraic structure, which is a commutative semiring and -semimodule. Moreover, both sets have the same property, which is isomorphic to the set of non-negative integers.

Collaboration network of the authors

9 authors · 12 co-authorship links

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Co-authorOrganisationJoint articles
Sena AriesandyAffiliation unknown1
Herlina NapitupuluAffiliation unknown1
Ati MaryatiAffiliation unknown1
Nursanti AnggrianiAffiliation unknown1
Edi KurniadiAffiliation unknown1
Henti HentiAffiliation unknown1

Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://ojs3.unpatti.ac.id/index.php/barekeng/oai, first harvested 5 Nov 2026, last seen 5 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en-US">ALGEBRAIC STRUCTURES ON A SET OF DISCRETE DYNAMICAL SYSTEM AND A SET OF PROFILE</dc:title>
	<dc:creator>Permatasari, Ananda Ayu</dc:creator>
	<dc:creator>Carnia, Ema</dc:creator>
	<dc:creator>Supriatna, Asep Kuswandi</dc:creator>
	<dc:description xml:lang="en-US">A discrete dynamical system is represented as a directed graph with graph nodes called states that can be seen on the dynamical map. This discrete dynamical system is symbolized by  , where  &amp;nbsp;is a finite set of states and the function g &amp;nbsp;is a function from  &amp;nbsp;to  . In the dynamical map, the discrete dynamical system has a height where the number of states in each height is called a profile. The set of discrete dynamical systems has an addition operation defined as a disjoint union on the graph and a multiplication operation defined as a tensor product on the graph. The set of discrete dynamical systems and the set of profiles are very interesting to observe from the algebraic point of view. Considering operation on the set of discrete dynamical systems and the set of profiles, we can see their algebraic structure. By recognizing the algebraic structure, it will be easy to solve the polynomial equation in the discrete dynamical system and in the profile. In this research, we will investigate the algebraic structure of discrete dynamical systems and the set of profiles. This research shows&amp;nbsp;that the set of discrete dynamical system has an algebraic structure, which is a commutative semiring and the set of profiles has an algebraic structure, which is a commutative semiring and  -semimodule. Moreover, both sets have the same property, which is isomorphic to the set of non-negative integers.</dc:description>
	<dc:publisher xml:lang="en-US">PATTIMURA UNIVERSITY</dc:publisher>
	<dc:date>2024-03-01</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9588</dc:identifier>
	<dc:identifier>10.30598/barekengvol18iss1pp0065-0074</dc:identifier>
	<dc:source xml:lang="en-US">BAREKENG: Jurnal Ilmu Matematika dan Terapan; Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application; 0065-0074</dc:source>
	<dc:source>2615-3017</dc:source>
	<dc:source>1978-7227</dc:source>
	<dc:source>10.30598/barekengvol18iss1year2024</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9588/7567</dc:relation>
	<dc:rights xml:lang="en-US">Copyright (c) 2024 Ananda Ayu Permatasari, Ema Carnia, Asep Kuswandi Supriatna</dc:rights>
	<dc:rights xml:lang="en-US">http://creativecommons.org/licenses/by-sa/4.0</dc:rights>
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