THE HISTORICAL EMERGENCE AND THEORETICAL FOUNDATIONS OF QUADRATIC STOCHASTIC OPERATORS.

Authors

  • Yashiyeva Feruza Yusuf qizi Author

Keywords:

Keywords: Quadratic Stochastic Operators (QSO), Nonlinear operators, Population genetics, Dynamical systems, Evolutionary models, Markov processes, Fixed points, Stability analysis, Ergodic theory, Measure-preserving transformations

Abstract

Abstract: Quadratic Stochastic Operators (QSOs) have played a pivotal role in the development of nonlinear dynamical systems theory, particularly within the context of population genetics and evolutionary processes. Originating from the early 20th century works on heredity and gene frequency models, QSOs generalize classical linear stochastic operators by incorporating quadratic terms that reflect pairwise interactions in populations. This paper reviews the historical emergence of QSOs, tracing their evolution from foundational biological problems to sophisticated mathematical frameworks.

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Published

2026-06-11

Issue

Vol. 70 No. 7 (2026): ЛУЧШИЕ ИНТЕЛЛЕКТУАЛЬНЫЕ ИССЛЕДОВАНИЯ | ЧАСТЬ-70 | ТОМ-7

Section

Articles