\xi^{(as)}-QUADRATIC STOCHASTIC OPERATORS IN TWO-DIMENSIONAL SIMPLEX AND THEIR BEHAVIOR

Alsarayreh, A.; Qaralleh, Izzat; Ahmad, Muhammad Zaini

doi:10.17654/nt039050737

Cited by 4 publications

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“…In addition, [29] has investigated a new subclass of QSOs on a finite-dimensional simplex. The trajectory behaviour of several classes of QSOs has been addressed in [30].…”

Section: Introductionmentioning

confidence: 99%

The nonlinear limit control of EDSQOs on finite dimensional simplex

et al. 2019

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Consensus problems in multi agent systems (MAS) are theoretical aspect convergence of doubly stochastic quadratic operators. This work has presented the dynamic classifications of extreme doubly stochastic quadratic operators (EDSQOs) on finite-dimensional simplex (FDS) based on the limit behaviour of the trajectories. The limit behaviour of the trajectories of EDSQOs, on FDS is either in state of convergence, or fixed or periodic. This paper aimed at examining the behaviour of these states. The paper modelled the states and proves theoretically the characteristics of each state. The results indicate that convergence operators converge to the centre 1 m , and EDSQOs point are fixed with two or more points whereas periodic states exhibit sinusoidal behaviour. This work has contributed in understanding the limit of EDSQOs of the exterior initial points as fixed and periodic points developed spread attribute toward a fixed point. ARTICLE HISTORY

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“…In addition, [29] has investigated a new subclass of QSOs on a finite-dimensional simplex. The trajectory behaviour of several classes of QSOs has been addressed in [30].…”

Section: Introductionmentioning

confidence: 99%

The nonlinear limit control of EDSQOs on finite dimensional simplex

et al. 2019

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“…In [28,29] ξ = of with point and trivial partitions of ∆ , respectively, as discussed by Alsarayreh, et al [33]. This indicates that all partitions of were investigated with respect to the point and trivial partitions of ∆ .…”

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confidence: 89%

Classification and Dynamics of Class of ξ(as)-QSO

El-Qader

Ghani

Qaralleh

2020

J. Math. Fund. Sci.

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“…Keywords: quadratic stochastic operator; nonlinear operator; Lebesgue measure; infinite state space; trajectory behavior 2010 MSC: 37A05, 37A50 Definition 1.1. A transformation V given by (1)…”

Section: Introductionmentioning

confidence: 99%

“…Investigating the trajectory behavior of nonlinear operators has been of interest since it was introduced decades ago for the purpose of understanding and describing a specific system. Readers may refer to the study of various nonlinear operators in both in a finite (see [1,9,11,17,18,19,20]) and an infinite state space (see [4,3,5,6,7,8,10,12,13,16,14,15]).…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Lebesgue Quadratic Stochastic Operator with Nonnegative Integers Parameters Generated by 2-PartitionSiti Nurlaili Karima, Nur Zatul Akmar Hamzahb, Nasir Ganikhodajevc, Muhammad Azrin Ahmadd, Norarida Abd RhanieaFaculty of Information and Communication Technology, Universiti Tunku Abdul Rahman, Kampar, Perak, Malaysia; bDepartment of Computational and Theoretical Sciences, International Islamic University Malaysia, Kuantan, Pahang, Malaysia; cInstitute of Mathematics, Uzbekistan Academy of Scie

2023

RNA

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The theory of quadratic stochastic operator (QSO) has been significantly developed since it was introduced in 1920s by Bernstein on population genetics. Over the century, many researchers have studied the behavior of such nonlinear operators by considering different classes of QSO on finite and infinite state spaces. However, all these studies do not comprehensively represent the core problem of QSO; i.e., the trajectory behavior. Recently, a class of QSO called Lebesgue QSO has been introduced and studied. Such an operator got its name based on Lebesgue measure which serves as a probability measure of the QSO. The conditions of the Lebesgue QSO have allowed us to consider the possibility of introducing a new measure for such QSO. This research presents a new class of Lebesgue QSO with nonnegative integers parameters generated by a measurable 2-partition on the continual state space X = [ , ] 0 1 . This research aims to study the trajectory behavior of the QSO by reducing its infinite variables into a mapping of one-dimensional simplex. The behavior of such operators will be investigated computationally and analytically, where the computational results conform to the analytical results. We will apply measure and probability theory as well as functional

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\xi^{(as)}-QUADRATIC STOCHASTIC OPERATORS IN TWO-DIMENSIONAL SIMPLEX AND THEIR BEHAVIOR

Cited by 4 publications

References 0 publications

The nonlinear limit control of EDSQOs on finite dimensional simplex

The nonlinear limit control of EDSQOs on finite dimensional simplex

Classification and Dynamics of Class of ξ(as)-QSO

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