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

Rawad Abdulghafor; Farruh Shahidi; Akram Zeki; Sherzod Turaev

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 509-519
- ISSN: 2391-5455

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topRawad Abdulghafor, et al. "Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex." Open Mathematics 14.1 (2016): 509-519. <http://eudml.org/doc/285534>.

@article{RawadAbdulghafor2016,

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.},

author = {Rawad Abdulghafor, Farruh Shahidi, Akram Zeki, Sherzod Turaev},

journal = {Open Mathematics},

keywords = {Doubly stochastic quadratic operators; Fixed point; Trajectory; Extreme point; Simplex; doubly stochastic quadratic operators; fixed point; trajectory; extreme point; simplex},

language = {eng},

number = {1},

pages = {509-519},

title = {Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex},

url = {http://eudml.org/doc/285534},

volume = {14},

year = {2016},

}

TY - JOUR

AU - Rawad Abdulghafor

AU - Farruh Shahidi

AU - Akram Zeki

AU - Sherzod Turaev

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

JO - Open Mathematics

PY - 2016

VL - 14

IS - 1

SP - 509

EP - 519

AB - 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.

LA - eng

KW - Doubly stochastic quadratic operators; Fixed point; Trajectory; Extreme point; Simplex; doubly stochastic quadratic operators; fixed point; trajectory; extreme point; simplex

UR - http://eudml.org/doc/285534

ER -

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