A convex combination of two quadratic stochastic operators acting in the $2D$-simplex
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 66-70.

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In this paper, we consider a quadratic operator on the two-dimensional simplex, which is a convex combination of two quadratic stochastic operators. It is proved that the center of the simplex is a unique fixed point of the operator and this fixed point is an attracting point.
Mots-clés : Simplex
Keywords: quadratic stochastic operators, convex combinations, fixed point.
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B. J. Mamurov. A convex combination of two quadratic stochastic operators acting in the $2D$-simplex. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2023), pp. 66-70. http://geodesic.mathdoc.fr/item/IVM_2023_7_a6/

[1] Bernstein S., “Solution of a mathematical problem connected with the theory of heredity”, Ann. Math. Stat., 13:1 (1942), 53–61 | DOI | MR | Zbl

[2] Rozikov U.A., Zhamilov U.U., “$F$-kvadratichnye stokhasticheskie operatory”, Matem. zametki, 83:4 (2008), 606–612 | DOI | MR | Zbl

[3] Zhamilov U.U., Rozikov U.A., “O dinamike strogo nevolterrovskikh kvadratichnykh stokhasticheskikh operatorov na dvumernom simplekse”, Matem. sb., 200:9 (2009), 81–94 | DOI | MR | Zbl

[4] Mamurov B.J., Rozikov U.A., “On cubic stochastic operators and processes”, J. Phys.: Conf. Ser., 697:1 (2016), 012017 | DOI

[5] Mamurov B.J., Rozikov U.A., Xudayarov S.S., “Quadratic stochastic processes of type $(\sigma | \mu)$”, Markov Processes Relat. Fields, 26 (2020), 915–933 | MR | Zbl

[6] Lyubich Y.I., Mathematical structures in population genetics, Biomathematics, 22, Springer, Berlin, 1992 | MR | Zbl

[7] Devaney R.L., An introduction to chaotic dynamical systems, Studies in Nonlinearity, Westview Press, Boulder, 2003 | MR | Zbl

[8] Vallander S., “O predelnom povedenii posledovatelnostei iteratsii nekotorykh kvadratichnykh preobrazovanii”, Dokl. Akademii nauk, 202:3 (1972), 515–517 | MR | Zbl

[9] Mamurov B.J., “Regularity of a non-Volterra quadratic stochastic operator on the $2$D simplex”, Ilm sarchashmalari, 11 (2022), 29–31