Qualitative behavior of rational difference equations of higher order

E. M. Elabbasya, A.A. Elsadanyb,* and Samia Ibrahimb

Qualitative behavior of rational difference equations of higher order

Authors :

E. M. Elabbasy^a,A.A. Elsadany^b,* and Samia Ibrahim^b

Author Address :

^aDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
^bDepartment of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt.

*Corresponding author.

Abstract :

In this paper we study the behavior of the solution of the following rational difference equation%
\begin{equation*}
x_{n+1}=\frac{ax_{n-r}^{2}+bx_{n-l}x_{n-k}^{2}}{%
cx_{n-r}^{2}+dx_{n-l}x_{n-k}^{2}}\text{ \ \ }n=0,1,...,
\end{equation*}
where the parameters $a,b,c$ and $d$ \ are positive real numbers and the initial conditions $x_{-t},x_{-t+1},...,x_{-1}$ and $x_{0}$ are posistive real numbers where $t=\max \{r,k,l\}.$

Keywords :

stability, rational difference equation, global attractor, periodic solution.

DOI :

Article Info :

Received : March 13, 2015; Accepted : August 13, 2015.