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2016 | 14 | 1 | 509-519
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Czasopismo
Rocznik
Tom
14
Numer
1
Strony
509-519
Opis fizyczny
Daty
wydano
2016-01-01
otrzymano
2015-04-27
zaakceptowano
2016-05-23
online
2016-07-26
Twórcy
  • Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100 Kuala Lumpur,, raaac2004@yahoo.com
  • Department of Mathematics, Pennsylvania State University UP, State College PA, 16801,, fus144@psu.edu
autor
  • Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100 Kuala Lumpur,, akramzeki@iium.edu.my
  • Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100 Kuala Lumpur,, sherzod@iium.edu.my
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_math-2016-0045
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