Qualitative behavior of rational difference equations of higher order

E. M. Elabbasy; A.A. Elsadany; Samia Ibrahim

doi:10.26637/mjm304/011

Abstract

In this paper we study the behavior of the solution of the following rational difference equation
$$
x_{n+1}=\frac{a x_{n-r}^2+b x_{n-l} x_{n-k}^2}{c x_{n-r}^2+d x_{n-l} x_{n-k}^2} \quad n=0,1, \ldots,
$$
where the parameters $a, b, c$ and $d$ are positive real numbers and the initial conditions $x_{-t}, x_{-t+1}, \ldots, x_{-1}$ and $x_0$ are posistive real numbers where $t=\max \{r, k, l\}$.

Keywords:

stability, rational difference equation, global attractor, periodic solution

Mathematics Subject Classification:

39A10

Authors Imprint References Funding Related Articles Downloads

E. M. Elabbasy Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt.
A.A. Elsadany Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt. https://orcid.org/0000-0002-5010-601X
Samia Ibrahim Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt.

Pages: 530-539
Date Published: 01-10-2015
Vol. 3 No. 04 (2015): Malaya Journal of Matematik (MJM)

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