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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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An $(\alpha,\beta)$- Quadratic Stochastic Operator Acting in $S^2$

Journal of Applied Nonlinear Dynamics 11(4) (2022) 777--788 | DOI:10.5890/JAND.2022.12.001

U.U. Jamilov$^{1,2,3}$, Kh. O. Khudoyberdiev$^{1}$

$^{1}$ V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University str., Tashkent, Uzbekistan

$^{2}$ Akfa University, 264, National Park str., Qibray district, 111221, Tashkent region, Uzbekistan

$^{3}$ National University of Uzbekistan, 4, University str., Tashkent, Uzbekistan

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In the present paper we consider a family of non-Volterra quadratic stochastic operators depending on the parameters $\alpha, \beta$ and study their trajectory behaviors. We find all fixed and periodic points for an $(\alpha,\beta)$- quadratic stochastic operator on the two-dimensional simplex. A complete description of the set of limit points is given, and we show that such operators have the ergodic property.


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