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A Class of Lotka-Volterra Operators with Historical Behavior

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Abstract

In the present paper, we consider a family of Lotka-Volterra operators which are discrete-time dynamical systems. It is established that each such kind of operator has historical behavior on any interior point of the two-dimensional simplex. In particularly, we solve the Takens’ problem within the introduced class of operators. Moreover, it will be shown that the LV-operators also have uniformly historic behavior.

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Acknowledgements

The second named author (F.M.) thanks the UAEU UPAR Grant No. G00003447 for support. The authors are greatly indebted to anonymous referee whose constructive comments/suggestions substantially contributed to improving the quality and presentation of this paper.

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Authors and Affiliations

  1. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 9, University str., 100174, Tashkent, Uzbekistan

    Uygun Jamilov

  2. Akfa University, 264, National Park Street, Barkamol MFY, Yangiabad village, 111221, Tashkent region, Qibray district, Uzbekistan

    Uygun Jamilov

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

    Uygun Jamilov

  4. College of Science, United Arab Emirates University, Al Ain, United Arab Emirates

    Farrukh Mukhamedov

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

    Farrukh Mukhamedov

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  1. Uygun Jamilov
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  2. Farrukh Mukhamedov
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Correspondence to Farrukh Mukhamedov.

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Jamilov, U., Mukhamedov, F. A Class of Lotka-Volterra Operators with Historical Behavior. Results Math 77, 169 (2022). https://doi.org/10.1007/s00025-022-01706-4

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