This article is cited in 2 papers

Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points

Sh. B. Abdurakhimova^a, U. A. Rozikov<sup>bcd

a</sup> Namangam State University
^b V. I. Romanovskiy Institute of Mathematcs of the Academy of Sciences of Uzbekistan
^c AKFA University
^d National University of Uzbekistan named after M. Ulugbek

Abstract: We consider a population consisting of two species whose dynamics is determined by a quadratic stochastic operator with variable coefficients, which makes it a discontinuous operator at two points. This operator depends on three parameters. The set of these parameters is divided into seven subsets. For each subset of parameters, we find fixed points, periodic points, and the set of limit points of trajectories generated by the respective quadratic stochastic operators.

Keywords: dynamical systems, fixed point, periodic point, limit point.

UDC: 517

Received: 10.07.2021
Revised: 26.12.2021

DOI: 10.4213/mzm13510

 English version: Mathematical Notes, 2022, 111:5, 676–687

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