Geometric quadratic stochastic operator on countable infinite set

Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

doi:10.1063/1.4907516

Cited by 11 publications

(5 citation statements)

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“…For a special case of parameters , of the QSO, study of the regularity of such operators. Comparing with previous studies for example in [5] the authors proved every quadratic stochastic operator generated by geometric distribution is a regular transformation. Moreover in [6] the authors also proved every quadratic stochastic operator generated by geometric distribution and three partitions with a different parameters is a regular transformation.…”

Section: Resultsmentioning

confidence: 71%

“…Moreover, it can be redefined on the set of all probability measures on a measurable state space. For example, a QSO generated by a family of pure geometric distributions was studied in [5,6], while QSO generated by pure Poisson distributions was studied in [7,8], and QSO generated by Gaussian distributions was studied in [9][10][11], and QSO generated by Lebesgue distributions was studied in [12,13] respectively. Some of applications of such QSO were established to generate algebra named as Rock-Paper-Scissor algebra [14].…”

Section: P I J Kmentioning

confidence: 99%

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On Three-Dimensional Mixing Geometric Quadratic Stochastic Operators

Ftameh¹,

Hee²

2021

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Section: Resultsmentioning

confidence: 71%

Section: P I J Kmentioning

confidence: 99%

On Three-Dimensional Mixing Geometric Quadratic Stochastic Operators

Ftameh¹,

Hee²

2021

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“…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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“…Over a century, the QSO study in a finite-dimensional simplex is still not depleted. Hence, many different classes of QSO are investigated (see for example [6][7][8][9][10][11][12][13]).…”

Section: Introductionmentioning

confidence: 99%

“…This study eventually opened up a path to studying different classes of QSO on infinite state space. One may refer to [8,9] for the QSO study on countable state space. For the study on continual state space, readers may refer to [10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%