On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl
El-Moneam, M., Zayed, E. (2015). On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl. EKB Journal Management System, 23(3), 494-499. doi: 10.1016/j.joems.2014.11.002
M.A. El-Moneam; E.M.E. Zayed. "On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl". EKB Journal Management System, 23, 3, 2015, 494-499. doi: 10.1016/j.joems.2014.11.002
El-Moneam, M., Zayed, E. (2015). 'On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl', EKB Journal Management System, 23(3), pp. 494-499. doi: 10.1016/j.joems.2014.11.002
El-Moneam, M., Zayed, E. On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl. EKB Journal Management System, 2015; 23(3): 494-499. doi: 10.1016/j.joems.2014.11.002

On the dynamics of the nonlinear rational difference equation xnþ1 ¼ Axn þ Bxnk þ Cxnl þ bxnk dxnkexnl

Journal of the Egyptian Mathematical Society
Volume 23, Issue 3, 2015, Pages 494-499    PDF (664.49 K)
Document Type: Original Article
DOI: 10.1016/j.joems.2014.11.002
Authors
M.A. El-Moneam* 1; E.M.E. Zayed2
1Mathematics Department, Faculty of Science and Arts in Farasan, Jazan University, Saudi Arabia
2Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Abstract
In this article, we study the periodicity, the boundedness and the global stability of the
positive solutions of the following nonlinear difference equation
xnþ1 ¼ Axn þ Bxnk þ Cxnl þ
bxnk
dxnk  exnl
; n ¼ 0; 1; 2; ...
where the coefficients A;B; C; b; d; e 2 ð0;1Þ, while k and l are positive integers. The initial
conditions xl; ... ; xk; ... ; x1; x0 are arbitrary positive real numbers such that k < l. Some
numerical examples will be given to illustrate our results.
Keywords
KEYWORDS Difference equations; Prime period two solution; Boundedness character; Locally asymptotically stable; Global attractor; Global stability
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