On a Family of Non-Volterra Quadratic Operators Acting on a Simplex

• Jamilov, Uygun ^[1] ; Ladra, Manuel ^[2]
  1. [1] Institute of Nuclear Physics

     Institute of Nuclear Physics

     Uzbekistán

     
  2. [2] Universidade de Santiago de Compostela

     Universidade de Santiago de Compostela

     Santiago de Compostela, España

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 3, 2020
• Idioma: inglés
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• Resumen

  • In the present paper, we consider a convex combination of non-Volterra quadratic stochastic operators defined on a finite-dimensional simplex depending on a parameter α and study their trajectory behaviours. We showed that for any α∈[0,1) the trajectories of such operator converge to a fixed point. For α=1 any trajectory of the operator converges to a periodic trajectory.