Separable quadratic stochastic operators

Rozikov, U. A.; Nazir, Shaheen

doi:10.1134/s1995080210030030

Cited by 6 publications

(3 citation statements)

References 12 publications

(21 reference statements)

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“…Certain other properties of such kind of operators has been studied in [13]. Some generalizations of Volterra QSO were studied in [14,21,22].…”

Section: On Volterra Qsomentioning

confidence: 99%

On Volterra and orthogonality preserving quadratic stochastic operators

Mukhamedov¹,

Taha²

2016

MMN

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A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Moreover, we provide its generalization in continuous setting. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

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“…Certain other properties of such kind of operators has been studied in [13]. Some generalizations of Volterra QSO were studied in [14,21,22].…”

Section: On Volterra Qsomentioning

confidence: 99%

On Volterra and orthogonality preserving quadratic stochastic operators

Mukhamedov¹,

Taha²

2016

MMN

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“…In [16] Separable Quadratic Stochastic Operators were introduced which is given as: The QSO (1), (2) with additional condition…”

Section: Preliminariesmentioning

confidence: 99%

On a class of separable quadratic stochastic operators

Rozikov¹,

Zada

2011

Lobachevskii J Math

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The purpose of this paper is to investigate a class of separable quadratic stochastic operators. Each separable quadratic stochastic operator (SQSO) depends on two quadratic matrices A and B, which have some relations. In this paper we proved that for each skew symmetric matrix A the corresponding SQSO is a linear operator. We also proved that non linear Volterra QSOs are not SQSOs. For a fixed matrix A we also discussed some properties of the set of all the corresponding matrices B of SQSOs.

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“…Certain other properties of such kind of operators has been studied in [15]. Some generalizations of Volterra QSO were studied in [16,22,23].…”

Section: On Volterra Qsomentioning

confidence: 99%

On orthogonality preserving quadratic stochastic operators

Mukhamedov¹,

Taha²

2015

AIP Conference Proceedings

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Abstract. A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Moreover, we provide its generalization in continuous setting. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

show abstract

Separable quadratic stochastic operators

Cited by 6 publications

References 12 publications

On Volterra and orthogonality preserving quadratic stochastic operators

On Volterra and orthogonality preserving quadratic stochastic operators

On a class of separable quadratic stochastic operators

On orthogonality preserving quadratic stochastic operators

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