CONVEX COMBINATIONS OF QUADRATIC STOCHASTIC OPERATORS

Authors

Boymatov Orif Ganiyevich

Keywords:

Quadratic stochastic operators, Convex combination, Dynamical systems, Fixed points, Stability, Functional analysis, Evolutionary models

Abstract

This chapter is dedicated to the theoretical investigation of convex combinations of quadratic stochastic operators (QSOs). It analyzes the mathematical construction, fundamental properties, and dynamic behavior of these convex combinations of QSOs. Specifically, the fixed points (equilibrium points) and stability issues of the combined operators are thoroughly examined. An analysis of existing literature evaluates the potential application of the convex combination concept to QSO theory. The obtained results propose novel approaches for modeling evolutionary processes and define directions for future research.

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References

Lyubich, Yu. I. Mathematical Structures in Population Genetics. Berlin: Springer Berlin Heidelberg, 1992.

Akin, E. The General Theory of Population Genetics. Berlin: Springer Berlin Heidelberg, 1979.

Ganikhodzhaev, R. N. "Quadratic stochastic operators, the asymptotic behavior of their trajectories." Russian Mathematical Surveys, vol. 64, no. 5, 2009, pp. 871-910.

Volkov, N. P. "On the structure of extreme quadratic stochastic operators." Mathematical Notes, vol. 93, no. 1, 2013, pp. 119-124.

Reed, D. J. "Existence of a measure for a Markov process in a population genetic model." Theoretical Population Biology, vol. 1, no. 1, 1970, pp. 264-284.

Reed, D. J. "Population genetic models and stochastic operators." Journal of Applied Probability, vol. 15, 1978, pp. 1-15.

Lyubich, Yu. I. "Basic concepts and theorems of the evolutionary genetics of free populations." Russian Mathematical Surveys, vol. 26, no. 5, 1971, pp. 51-123.

Mendel, G. "Versuche über Pflanzen-Hybriden." Verhandlungen des naturforschenden Vereines in Brünn, Bd. IV, 1865, pp. 3-47.

Alimov, G. V. "On the dynamics of quadratic stochastic operators of a special type." Uzbek Mathematical Journal, no. 3, 1998, pp. 12-19.

Mukhamedov, F., and Rozikov, U. "On quadratic stochastic operators generated by Gibbs distributions." Journal of Physics A: Mathematical and Theoretical, vol. 42, 2009, 095001.

Alimov, G. V., and Ganikhodzhaev, R. N. "Quadratic stochastic operators and their applications in population genetics." Mathematical Biosciences, vol. 185, 2003, pp. 117-132.

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Published

2026-01-31

How to Cite

Boymatov Orif Ganiyevich. (2026). CONVEX COMBINATIONS OF QUADRATIC STOCHASTIC OPERATORS. International Multidisciplinary Journal for Research & Development, 13(01), 1044–1048. Retrieved from https://ijmrd.in/index.php/imjrd/article/view/4959