Qualitative study of a higher order rational difference equation

Yıl 2018, Cilt: 47 Sayı: 5, 1128 - 1143, 16.10.2018

Abdul Khaliq E.m. Elsayed

Öz

In this paper we study the behavior of the difference equation

                     $x_{n+1}$ = $\dfrac{\alpha x_nx_{n-l}}{\beta x_{n-m}+\gamma x_{n-l}}$,$\quad n=0,1,$ $\cdots$

where the initial conditions $x_{-r}$, $x_{-r+1}$, $\cdots$ ,$x_0$ are arbitrary non zero real numbers where $r=\max\{l,m\}$ is a non-negative integer and  $\alpha$, $\beta$ and $\gamma$ are constants: Also, we obtain the solutions of some special cases of this equation. At the end we present some numerical examples to support our theoretical discussion.

Anahtar Kelimeler

difference equation, stability, boundedness, global attractivity

Kaynakça

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