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Genetic Algebras Associated with ξ(-Quadratic Stochastic Operators
Farrukh Mukhamedov1, Izzat Qaralleh2, Taimun Qaisar1
1Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain P.O. Box 15551, United Arab Emirates.
Entropy (Basel, Switzerland)
|June 28, 2023
Summary
This study examines ξ(a)-quadratic stochastic operators (QSOs) and their associated genetic algebras. Researchers explored algebraic properties like associativity and derivations, revealing isomorphic structures and dynamic behaviors.
Area of Science:
- Algebraic theory
- Stochastic processes
- Dynamical systems
Background:
- Quadratic stochastic operators (QSOs) are fundamental in probability and population genetics.
- Understanding the algebraic structures of genetic algebras associated with QSOs is crucial for analyzing their behavior.
Purpose of the Study:
- To investigate the algebraic properties of genetic algebras linked to ξ(a)-quadratic stochastic operators (QSOs).
- To analyze the dynamic behavior of these operators on a two-dimensional simplex.
Main Methods:
- Focus on a specific partition of QSOs leading to three nonconjugate classes.
- Analysis of genetic algebras derived from these classes, examining associativity, characters, and derivations.
- Exploration of the dynamic behavior of the operators.
Main Results:
- Demonstrated that genetic algebras arising from the identified classes are isomorphic.
- Provided conditions for associativity and character behavior within these genetic algebras.
- Characterized the dynamic behavior of the ξ(a)-QSOs.
Conclusions:
- The study establishes a clear link between the algebraic properties of genetic algebras and the dynamics of ξ(a)-QSOs.
- The findings contribute to a deeper understanding of stochastic operators and their applications.
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