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On Separable Cubic Stochastic Operators

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Abstract

In this paper, we explore separable cubic stochastic operators defined on a finite-dimensional simplex, which depend on three matrices. We have developed Lyapunov functions under specific conditions that influence the entries of these matrices. These functions enable us to establish upper bounds for the \(\omega \)-limit set of the trajectories. We also present a sufficient condition for identifying these operators as Lotka–Volterra operators. For separable cubic stochastic operators defined on the 2D simplex, we provide descriptions of their fixed points and their respective types. Moreover, we demonstrate that, under certain parameter conditions, these operators exhibit regular behavior.

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Acknowledgements

The authors would like to thank the anonymous referees for their comments and suggestions that contributed to improve this paper.

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Authors and Affiliations

  1. Karshi State University, 17, Ko’chabog’ str., 180100, Karshi, Uzbekistan

    B. S. Baratov

  2. V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University str., 100174, Tashkent, Uzbekistan

    U. U. Jamilov

  3. Central Asian University, 264, National Park Street, 111221, Tashkent, Uzbekistan

    U. U. Jamilov

  4. National University of Uzbekistan, 4, University str., 100174, Tashkent, Uzbekistan

    U. U. Jamilov

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  1. B. S. Baratov
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Correspondence to U. U. Jamilov.

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Baratov, B.S., Jamilov, U.U. On Separable Cubic Stochastic Operators. Qual. Theory Dyn. Syst. 23, 93 (2024). https://doi.org/10.1007/s12346-023-00950-5

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