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The Dynamics of a Volterra Cubic Operator

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Infinite Dimensional Analysis, Quantum Probability and Applications (ICQPRT 2021)

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Abstract

In this paper, we consider a family of Volterra cubic stochastic operators defined on the two-dimensional simplex depending on two parameters. It is found all fixed points and their types. It is proved that depending on the parameters and an initial point a trajectory of such kind operator converges to a vertex of the two-dimensional simplex.

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Authors and Affiliations

  1. V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University Str., 100174, Tashkent, Uzbekistan

    Uygun U. Jamilov

  2. AKFA University, 264, National Park Str., 111221, Qibray district, Tashkent region, Uzbekistan

    Uygun U. Jamilov

  3. National University of Uzbekistan, 4, University Str., 100174, Tashkent, Uzbekistan

    Uygun U. Jamilov

  4. Navoi State Pedagogical Institute, 45, Ibn Sino street, Navoi, Uzbekistan

    Elbek Kh. Ziyodullaev

Authors
  1. Uygun U. Jamilov
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  2. Elbek Kh. Ziyodullaev
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Correspondence to Uygun U. Jamilov .

Editor information

Editors and Affiliations

  1. Vito Volterra Interdepartamental Centre, Universita degli Studi di Roma, Rome, Italy

    Luigi Accardi

  2. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, Abu Dhabi, United Arab Emirates

    Farrukh Mukhamedov

  3. Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, Abu Dhabi, United Arab Emirates

    Ahmed Al Rawashdeh

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Jamilov, U.U., Ziyodullaev, E.K. (2022). The Dynamics of a Volterra Cubic Operator. In: Accardi, L., Mukhamedov, F., Al Rawashdeh, A. (eds) Infinite Dimensional Analysis, Quantum Probability and Applications. ICQPRT 2021. Springer Proceedings in Mathematics & Statistics, vol 390. Springer, Cham. https://doi.org/10.1007/978-3-031-06170-7_22

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