## Qualitative Behavior of a Quadratic Second-Order Rational Difference Equation -by M. B. Almatrafi, E. M. Elsayed and Faris Alzahrani

Abstract: This article demonstrates the existence of boundedness, asymptotic behavior and the periodicity of the following quadratic second-order rational difference equation: \begin{equation*} x_{n+1}=ax_{n}+\dfrac{bx_{n}^{2}+cx_{n}x_{n-1}+dx_{n-1}^{2}}{\alpha x_{n}^{2}+\beta x_{n}x_{n-1}+\gamma x_{n-1}^{2}},\;\;\;n=0,1,..., \end{equation*} where the constants $a,\ b,\ c,\ d,\ \alpha ,\ \beta $ and $\gamma $ are positive real numbers and...