Affiliation:
1. Mathematics Department, Faculty of Science, Jazan University, Kingdom of Saudi Arabia.
Abstract
In this paper, we discuss some qualitative properties of the positive solutions to the following rational nonlinear difference equation ${x_{n+1}}=% \frac{{\alpha {x_{n-m}+\eta {x_{n-k}{+\sigma {x_{n-l}}}}+}}\delta {{x_{n}}}}{% {\beta +\gamma {x_{n-k}}{x_{n-l}}\left( {{x_{n-k}}+{x_{n-l}}}\right) }}$, $% n=0,1,2,...$ where the parameters $\alpha ,\beta ,\gamma ,\delta ,{\eta },{% \sigma }\in (0,\infty )$, while $m,k,l$ are positive integers, such that $% m
Publisher
Fundamental Journal of Mathematics and Applications
Reference34 articles.
1. [1] R. P. Agarwal, E. M. Elsayed, On the solution of fourth-order rational recursive sequence, Adv. Stud. Contemp. Math., 20(4) (2010), 525--545.
2. [2] A. M. Alotaibi, M. A. El-Moneam, On the dynamics of the nonlinear rational difference equation ${\ x_{n+1}}=\frac{{\alpha {x_{n-m}+}}% \delta {{x_{n}}}}{{\beta +\gamma {x_{n-k}}{\ x_{n-l}}\left( {{x_{n-k}}+{% x_{n-l}}}\right) }}$, AIMS Mathematics, 7(5) (2022), 7374--7384.
3. [3] R. Devault, W. Kosmala, G. Ladas, S. W. Schaultz, Global behavior of $y_{n+1}=\dfrac{p+y_{n-k}}{qy_{n}+y_{n-k}}$, Nonlinear Anal. Theory Methods Appl., 47 (2004), 83--89.
4. [4] Q. Din, Dynamics of a discrete Lotka-Volterra model, Adv. Differ. Equ., 95 (2013).
5. [5] Q. Din, On a system of rational difference equation, Demonstratio Mathematica, (in press).