On the Equiprobable Strictly Non-Volterra Quadratic Stochastic Operators

  1. U. U. Jamilov 1
  2. M. Ladra 2
  3. R. T. Mukhitdinov 3
  1. 1 National University of Uzbekistan (Uzbekistán)
  2. 2 Universidade de Santiago de Compostela
    info

    Universidade de Santiago de Compostela

    Santiago de Compostela, España

    ROR https://ror.org/030eybx10

  3. 3 Bukhara State University (Uzbekistán)
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Journal:
Qualitative theory of dynamical systems

ISSN: 1575-5460

Year of publication: 2017

Volume: 16

Issue: 3

Pages: 645-655

Type: Article

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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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Acknowledgements 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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