Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite- dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation...

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Main Authors:	Abdulghafor, Rawad Abdulkhaleq Abdulmolla, Shahidi, Farruh, Zeki, Akram M., Turaev, Sherzod
Format:	Article
Language:	English English English
Published:	De Gruyter Open Ltd. 2016
Subjects:	QA Mathematics QA75 Electronic computers. Computer science
Online Access:	http://irep.iium.edu.my/53705/ http://irep.iium.edu.my/53705/ http://irep.iium.edu.my/53705/ http://irep.iium.edu.my/53705/1/%5BOpen%20Mathematics%5D%20Dynamics%20of%20doubly%20stochastic%20quadratic%20operators%20on%20a%20finite-dimensional%20simplex.pdf http://irep.iium.edu.my/53705/7/53705_Dynamics%20of%20doubly%20stochastic_WOS.pdf http://irep.iium.edu.my/53705/8/53705_Dynamics%20of%20doubly%20stochastic_SCOPUS.pdf

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spelling	iium-537052019-05-24T01:23:00Z http://irep.iium.edu.my/53705/ Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex Abdulghafor, Rawad Abdulkhaleq Abdulmolla Shahidi, Farruh Zeki, Akram M. Turaev, Sherzod QA Mathematics QA75 Electronic computers. Computer science The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite- dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex. De Gruyter Open Ltd. 2016-07-26 Article PeerReviewed application/pdf en http://irep.iium.edu.my/53705/1/%5BOpen%20Mathematics%5D%20Dynamics%20of%20doubly%20stochastic%20quadratic%20operators%20on%20a%20finite-dimensional%20simplex.pdf application/pdf en http://irep.iium.edu.my/53705/7/53705_Dynamics%20of%20doubly%20stochastic_WOS.pdf application/pdf en http://irep.iium.edu.my/53705/8/53705_Dynamics%20of%20doubly%20stochastic_SCOPUS.pdf Abdulghafor, Rawad Abdulkhaleq Abdulmolla and Shahidi, Farruh and Zeki, Akram M. and Turaev, Sherzod (2016) Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex. Open Mathematics, 14 (1). pp. 509-519. ISSN 2391-5455 https://www.degruyter.com/downloadpdf/j/math.2016.14.issue-1/math-2016-0045/math-2016-0045.xml 10.1515/math-2016-0045
repository_type	Digital Repository
institution_category	Local University
institution	International Islamic University Malaysia
building	IIUM Repository
collection	Online Access
language	English English English
topic	QA Mathematics QA75 Electronic computers. Computer science
spellingShingle	QA Mathematics QA75 Electronic computers. Computer science Abdulghafor, Rawad Abdulkhaleq Abdulmolla Shahidi, Farruh Zeki, Akram M. Turaev, Sherzod Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
description	The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite- dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We show that if d.s.q.o. is not a permutation then it has no periodic points on the interior of the two dimensional (2D) simplex. We also show that this property fails in higher dimensions. In addition, the paper also discusses the dynamics classifications of extreme points of d.s.q.o. on two dimensional simplex. As such, we provide some examples of d.s.q.o. which has a property that the trajectory of any initial point tends to the center of the simplex. We also provide and example of d.s.q.o. that has infinitely many fixed points and has infinitely many invariant curves. We therefore came-up with a number of evidences. Finally, we classify the dynamics of extreme points of d.s.q.o. on 2D simplex.
format	Article
author	Abdulghafor, Rawad Abdulkhaleq Abdulmolla Shahidi, Farruh Zeki, Akram M. Turaev, Sherzod
author_facet	Abdulghafor, Rawad Abdulkhaleq Abdulmolla Shahidi, Farruh Zeki, Akram M. Turaev, Sherzod
author_sort	Abdulghafor, Rawad Abdulkhaleq Abdulmolla
title	Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
title_short	Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
title_full	Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
title_fullStr	Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
title_full_unstemmed	Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
title_sort	dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
publisher	De Gruyter Open Ltd.
publishDate	2016
url	http://irep.iium.edu.my/53705/ http://irep.iium.edu.my/53705/ http://irep.iium.edu.my/53705/ http://irep.iium.edu.my/53705/1/%5BOpen%20Mathematics%5D%20Dynamics%20of%20doubly%20stochastic%20quadratic%20operators%20on%20a%20finite-dimensional%20simplex.pdf http://irep.iium.edu.my/53705/7/53705_Dynamics%20of%20doubly%20stochastic_WOS.pdf http://irep.iium.edu.my/53705/8/53705_Dynamics%20of%20doubly%20stochastic_SCOPUS.pdf
first_indexed	2023-09-18T21:15:56Z
last_indexed	2023-09-18T21:15:56Z
_version_	1777411562662789120

Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex

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