MMN-3996

Global dynamical behaviours and periodicity of a certain quadratic-rational difference equation with delay

  • E. Tasdemir, Kırklareli University, Pınarhisar Vocational School, 39300, Kırklareli, Turkey, erkantasdemir@hotmail.com
  • M. Göcen, Zonguldak Bülent Ecevit University, Department of Mathematics, Art and Science Faculty, 67100, Zonguldak, Turkey, gocenm@hotmail.com
  • Y. Soykan, Zonguldak Bülent Ecevit University, Department of Mathematics, Art and Science Faculty, 67100, Zonguldak, Turkey, yuksel.soykan@hotmail.com

Abstract

Our aim in this paper is to deal with the dynamics of following higher order difference equation% \begin{equation*} x_{n+1}=A+B\frac{x_{n-m}}{x_{n}^{2}} \end{equation*}% where $A,B>0$, and initial values are positive, and $m=\{1,2,...\}$\textbf{.} Furthermore, we discuss the periodicity, boundedness, semi-cycles, global asymptotic stability of solutions of these equations. We also handle the rate of convergence of solutions of these difference equations.


Vol. 23 (2022), No. 1, pp. 471-484
DOI: 10.18514/MMN.2022.3996


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