Geometric quadratic stochastic operator on countable infinite set

2015 ◽  
Author(s):  
Nasir Ganikhodjaev ◽  
Nur Zatul Akmar Hamzah
Keyword(s):  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Infinite Set

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 Regularity of Geometric quadratic stochastic operator generated by 2-partition of infinite points

2020 ◽  
Vol 16 (3) ◽  
pp. 281-285
Author(s):  
Siti Nurlaili Karim ◽  
Nur Zatul Akmar Hamzah ◽  
Nasir Ganikhodjaev
Keyword(s):  
Fixed Point ◽  
State Space ◽  
Unique Fixed Point ◽  
Limiting Behavior ◽  
Countable State Space ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Countable State ◽  
Regular Transformation

In this research, we construct a class of quadratic stochastic operator called Geometric quadratic stochastic operator generated by arbitrary 2-partition  of infinite points on a countable state space , where . We also study the limiting behavior of such operator by proving the existence of the limit of the sequence  through the convergence of the trajectory to a unique fixed point. It is established that such operator is a regular transformation.

scholarly journals F-evolution algebra

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2637-2652 ◽  
Author(s):  
Uygun Jamilov ◽  
Manuel Ladra
Keyword(s):  
Fixed Point ◽  
Banach Algebra ◽  
Necessary Conditions ◽  
Zero Point ◽  
Limit Set ◽  
Volterra Type ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Evolution Algebra ◽  
Upper Estimate

We consider the evolution algebra of a free population generated by an F-quadratic stochastic operator. We prove that this algebra is commutative, not associative and necessarily power-associative. We show that this algebra is not conservative, not stationary, not genetic and not train algebra, but it is a Banach algebra. The set of all derivations of the F-evolution algebra is described. We give necessary conditions for a state of the population to be a fixed point or a zero point of the F-quadratic stochastic operator which corresponds to the F-evolution algebra. We also establish upper estimate of the ?-limit set of the trajectory of the operator. For an F-evolution algebra of Volterra type we describe the full set of idempotent elements and the full set of absolute nilpotent elements.

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.

scholarly journals THE ASYMPTOTIC BEHAVIOR OF TRAJECTORIES OF DISSIPATIVE QUADRATIC STOCHASTIC OPERATORS ON 2D SIMPLEX

2012 ◽  
Vol 09 ◽  
pp. 293-298
Author(s):  
FARRUH SHAHIDI ◽  
ABU OSMAN MD TAP
Keyword(s):  
Fixed Point ◽  
Asymptotic Behavior ◽  
Fixed Points ◽  
Unique Fixed Point ◽  
Limit Behavior ◽  
Quadratic Stochastic Operator ◽  
Stochastic Operator ◽  
Quadratic Stochastic Operators ◽  
The Face

In the present paper we study limit behavior of dissipative quadratic stochastic operators on 2D simplex. We show that dissipative quadratic stochastic operator, which is not linear, is either regular or has infinitely many fixed points. If dissipative quadratic stochastic operator is regular, it is shown that its unique fixed point is either a vertex of the simplex or the center of the face of the simplex.

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