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Behavior of Solutions of a Fourth Order Difference Equation
Abo-Zeid, Raafat Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.2
In this paper, we introduce an explicit formula for the solutions and discuss the global behavior of solutions of the difference equation $$x_{n+1}={\frac{ax_{n-3}}{b-cx_{n-1}x_{n-3}}}$$, $n=0,1,{\ldots}$ where a, b, c are positive real numbers and the initial conditions $x_{-3}$, $x_{-2}$, $x_{-1}$, $x_0$ are real numbers.
Dynamical Behavior of a Third-Order Difference Equation with Arbitrary Powers
Gumus, Mehmet,Abo-Zeid, Raafat,Ocalan, Ozkan Department of Mathematics 2017 Kyungpook mathematical journal Vol.57 No.2
The aim of this paper is to investigate the dynamical behavior of the difference equation $$x_{n+1}={\frac{{\alpha}x_n}{{\beta}+{\gamma}x^p_{n-1}x^q_{n-2}}},\;n=0,1,{\ldots}$$, where the parameters ${\alpha}$, ${\beta}$, ${\gamma}$, p, q are non-negative numbers and the initial values $x_{-2}$, $x_{-1}$, $x_0$ are positive numbers. Also, some numerical examples are given to verify our theoretical results.
On a Higher-Order Rational Difference Equation
Farida Belhannache,Nouressadat Touafek,Raafat Abo-Zeid 한국전산응용수학회 2016 Journal of applied mathematics & informatics Vol.34 No.5
In this paper, we investigate the global behavior of the solutions of the difference equation \begin{equation*} x_{n+1}=\frac{A+B x_{n-2k-1}}{C+D \prod^{k}_{i=l}x_{n-2i}^{m_{i}}},\text{ }n=0,1,..., \end{equation*}% with non-negative initial conditions, the parameters $A,$ $B$ are non-negative real numbers, $C$, $D$ are positive real numbers, $k,$ $l$ are fixed non-negative integers such that $l\leq k$, and $m_{i}, i=\overline{l,k}$ are positive integers.
ON A HIGHER-ORDER RATIONAL DIFFERENCE EQUATION
BELHANNACHE, FARIDA,TOUAFEK, NOURESSADAT,ABO-ZEID, RAAFAT The Korean Society for Computational and Applied M 2016 Journal of applied mathematics & informatics Vol.34 No.5
In this paper, we investigate the global behavior of the solutions of the difference equation $x_{n+1}=\frac{A+Bx_{n-2k-1}}{C+D\prod_{i=l}^{k}x_{n-2i}^{m_i}}$, n=0, 1, ..., with non-negative initial conditions, the parameters A, B are non-negative real numbers, C, D are positive real numbers, k, l are fixed non-negative integers such that l ≤ k, and m<sub>i</sub>, i=l, k are positive integers.