Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators

Farrukh Mukhamedov, Izzat Qaralleh, Taimun Qaisar, Mahmoud Alhaj Hasan

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

The present paper deals with a class of (Formula presented.) -quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with (Formula presented.) -QSOs. Namely, the associativity, characters and derivations of genetic algebras are studied. Moreover, the dynamics of these operators are also explored. Specifically, we focus on a particular partition that results in nine classes, which are further reduced to three nonconjugate classes. Each class gives rise to a genetic algebra denoted as (Formula presented.), and it is shown that these algebras are isomorphic. The investigation then delves into analyzing various algebraic properties within these genetic algebras, such as associativity, characters, and derivations. The conditions for associativity and character behavior are provided. Furthermore, a comprehensive analysis of the dynamic behavior of these operators is conducted.

Original languageEnglish
Article number934
JournalEntropy
Volume25
Issue number6
DOIs
Publication statusPublished - Jun 2023

Keywords

  • associativity
  • dynamics
  • quadratic stochastic operator

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Electrical and Electronic Engineering

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