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

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 A note on the entropy of a doubly stochastic operator

2000 ◽  
Vol 84 (1) ◽  
pp. 245-254 ◽  
Author(s):  
Brunon Kamiński ◽  
José de Sam Lazaro
Keyword(s):  
Doubly Stochastic ◽  
Stochastic Operator ◽  
Doubly Stochastic Operator

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.

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