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

• Autorzy: Rawad Abdulghafor , Farruh Shahidi , Akram Zeki , Sherzod Turaev
• 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.

Słowa kluczowe

EN

Doubly stochastic quadratic operators; Fixed point; Trajectory; Extreme point; Simplex

Kategorie tematyczne

• 46T99: None of the above, but in this section
• 46A55: Convex sets in topological linear spaces; Choquet theory
• 15A63: Quadratic and bilinear forms, inner products \SeeMainly{}

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 509-519

Daty

wydano

2016-01-01

otrzymano

2015-04-27

zaakceptowano

2016-05-23

online

2016-07-26

Twórcy

autor

Rawad Abdulghafor

• Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100 Kuala Lumpur,

autor

Farruh Shahidi

• Department of Mathematics, Pennsylvania State University UP, State College PA, 16801,

autor

Akram Zeki

• Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100 Kuala Lumpur,

autor

Sherzod Turaev

• Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, 53100 Kuala Lumpur,

Identyfikatory

DOI

10.1515/math-2016-0045