Dynamics of the System of Difference Equations xn+1=A+yn-kyn,yn+1=B+xn-kxn

• Abualrub, S ^[1] ; Aloqeili, M ^[1]
  1. [1] Birzeit University

     Birzeit University

     Territorios Palestinos

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 19, Nº 2, 2020
• Idioma: inglés
• DOI: 10.1007/s12346-020-00408-y
• Enlaces
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• Resumen

  • In this paper, we solve open problem 1 in Gumuş (Differ Equ Appl 24(6):976–991 2018). We investigate the oscillatory behavior, boundedness, persistence of positive solutions and the global asymptotic stability of the unique positive equilibrium point of the system of two rational difference equations: xn+1=A+yn-kyn,yn+1=B+xn-kxn,n=0,1,…where the parameters A>0 and B>0, the initial conditions xi,yi are arbitrary positive numbers for i=-k,-k+1,…,0 and k∈Z+. Moreover, we give some numerical examples that support our analytical results.

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