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On the Equiprobable Strictly Non-Volterra Quadratic Stochastic Operators

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Abstract

In this paper we consider an equiprobable strictly non-Volterra quadratic stochastic operator defined on a finite-dimensional simplex. We show that such an operator has a unique fixed point, which is an attracting fixed point. Furthermore, we construct a Lyapunov function and use it in order to prove that for any initial point the set of limit points of the trajectory is a singleton.

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Acknowledgments

The authors would like to thank the referees for their comments and suggestions that contributed to improve this paper. This work was partially supported by a grant from the Niels Henrik Abel Board and by Ministerio de Economía y Competitividad (Spain), Grant MTM2013-43687-P (European FEDER support included) and by Xunta de Galicia, Grant GRC2013-045 (European FEDER support included). The first author thanks the University of Santiago de Compostela (USC), Spain, for the kind hospitality and for providing all facilities.

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Authors and Affiliations

  1. Institute of Mathematics, National University of Uzbekistan, 100125, Tashkent, Uzbekistan

    U. U. Jamilov

  2. Department of Algebra, University of Santiago de Compostela, 15782, Santiago de Compostela, Spain

    M. Ladra

  3. Faculty of Mathematics and Physics, Bukhara State University, 705018, Bukhara, Uzbekistan

    R. T. Mukhitdinov

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  1. U. U. Jamilov
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  2. M. Ladra
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  3. R. T. Mukhitdinov
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Correspondence to M. Ladra.

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Jamilov, U.U., Ladra, M. & Mukhitdinov, R.T. On the Equiprobable Strictly Non-Volterra Quadratic Stochastic Operators. Qual. Theory Dyn. Syst. 16, 645–655 (2017). https://doi.org/10.1007/s12346-016-0209-9

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  • DOI: https://doi.org/10.1007/s12346-016-0209-9

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