On the Equiprobable Strictly Non-Volterra Quadratic Stochastic Operators

• U. U. Jamilov ^[1] ; M. Ladra ^[2] ; R. T. Mukhitdinov ^[3]
  1. [1] National University of Uzbekistan

     National University of Uzbekistan

     Uzbekistán

     
  2. [2] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
  3. [3] Bukhara State University

     Bukhara State University

     Uzbekistán

     

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• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 16, Nº 3, 2017, págs. 645-655
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.