scholarly journals On orthogonality preserving cubic stochastic operator defined on 1-dimensional simplex

2019 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Chin Hee Pah ◽  
Azizi Rosli
Keyword(s):  
Dimensional Simplex ◽  
Stochastic Operator

ON DYNAMICS OF ℓ-VOLTERRA QUADRATIC STOCHASTIC OPERATORS

2010 ◽  
Vol 03 (02) ◽  
pp. 143-159 ◽  
Author(s):  
U. A. ROZIKOV ◽  
A. ZADA
Keyword(s):  
Volterra Operator ◽  
Periodic Points ◽  
Dimensional Simplex ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Volterra Operators ◽  
Quadratic Stochastic Operators

We introduce a notion of ℓ-Volterra quadratic stochastic operator defined on (m - 1)-dimensional simplex, where ℓ ∈ {0,1,…, m}. The ℓ-Volterra operator is a Volterra operator if and only if ℓ = m. We study structure of the set of all ℓ-Volterra operators and describe their several fixed and periodic points. For m = 2 and 3, we describe behavior of trajectories of (m - 1)-Volterra operators. The paper also contains many remarks with comparisons of ℓ-Volterra operators and Volterra ones.

scholarly journals Strictly non-Volterra quadratic stochastic operator (QSO) on 3-dimensional simplex

2018 ◽  
Author(s):  
Nasir Ganikhodjaev ◽  
Siti Hasanah Bt Jusoo
Keyword(s):  
Dimensional Simplex ◽  
3 Dimensional ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator

scholarly journals Necessary and Sufficient Conditions for Complementary Stochastic Quadratic Operators of Finite-Dimensional Simplex

2017 ◽  
Vol 1 (1) ◽  
pp. 22 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki
Keyword(s):  
Dimensional Space ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Finite Dimensional Space ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Quadratic Stochastic Operator ◽  
Finite Dimensional ◽  
Stochastic Operator ◽  
Necessary And Sufficient

We define a complementary stochastic quadratic operator on finite-dimensional space as a new sub-class of quadratic stochastic operator. We give necessary and sufficient conditions for complementary stochastic quadratic operator.  

scholarly journals Onξ(s)-Quadratic Stochastic Operators on Two-Dimensional Simplex and Their Behavior

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov ◽  
Izzat Qaralleh
Keyword(s):  
Time Evolution ◽  
General Problem ◽  
Operator Theory ◽  
Nonlinear Operator ◽  
Two Dimensional ◽  
Dimensional Simplex ◽  
Nonlinear Operators ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators

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. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for quadratic stochastic operators which are the simplest nonlinear operators. To study this problem, several classes of QSO were investigated. We studyξ(s)-QSO defined on 2D simplex. We first classifyξ(s)-QSO into 20 nonconjugate classes. Further, we investigate the dynamics of three classes of such operators.

On a Volterra Cubic Stochastic Operator

2017 ◽  
Vol 80 (2) ◽  
pp. 319-334 ◽  
Author(s):  
U. U. Jamilov ◽  
A. Yu. Khamraev ◽  
M. Ladra
Keyword(s):  
Stochastic Operator

On a Non-Volterra Cubic Stochastic Operator

2021 ◽  
Vol 42 (12) ◽  
pp. 2800-2807
Author(s):  
U. U. Jamilov ◽  
K. A. Kurganov
Keyword(s):  
Stochastic Operator

scholarly journals On Minimal Absorption Index for an n-Dimensional Simplex

2018 ◽  
Vol 25 (1) ◽  
pp. 140-150 ◽  
Author(s):  
Mikhail V. Nevskii ◽  
Alexey Y. Ukhalov
Keyword(s):  
Absorption Index ◽  
Dimensional Simplex

Linear Stochastic Operator Equations

1984 ◽  
pp. 147-196
Author(s):  
A. V. Skorohod
Keyword(s):  
Operator Equations ◽  
Stochastic Operator
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