- Hacettepe Journal of Mathematics and Statistics
- Vol: 47 Issue: 5
- Qualitative study of a higher order rational difference equation
Qualitative study of a higher order rational difference equation
Authors : Abdul Khaliq, E. M. Elsayed
Pages : 1128-1143
View : 12 | Download : 6
Publication Date : 2018-10-16
Article Type : Research
Abstract :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.Keywords : difference equation, stability, boundedness, global attractivity