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Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points

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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.

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Acknowledgments

The authors wish to express gratitude to the referee for carefully reading the paper and helpful comments.

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Correspondence to Sh. B. Abdurakhimova.

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Translated from Matematicheskie Zametki, 2022, Vol. 111, pp. 663–675 https://doi.org/10.4213/mzm13510.

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Abdurakhimova, S.B., Rozikov, U.A. Dynamical System of a Quadratic Stochastic Operator with Two Discontinuity Points. Math Notes 111, 676–687 (2022). https://doi.org/10.1134/S0001434622050029

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  • DOI: https://doi.org/10.1134/S0001434622050029

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