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

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

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Abstract

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.

Item Type:	Article (Journal)
Additional Information:	6574/53705
Uncontrolled Keywords:	Doubly stochastic quadratic operators, fixed point, trajectory, extreme point, simplex
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button):	Kulliyyah of Information and Communication Technology Kulliyyah of Information and Communication Technology Kulliyyah of Information and Communication Technology > Department of Computer Science Kulliyyah of Information and Communication Technology > Department of Computer Science
Depositing User:	Dr. Sherzod Turaev
Date Deposited:	30 Dec 2016 13:52
Last Modified:	24 May 2019 09:23
URI:	http://irep.iium.edu.my/id/eprint/53705

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