Stability of the third order rational difference equation

Abstract

In this paper, we examine the global stability and boundedness of the difference equation \[ x_{n+1}=\frac{\alpha x_{n}x_{n-1}+\beta x_{n}x_{n-2}}{\gamma {x}_{n-1}+\theta {x}_{n-2}}\] where the initial conditions are non zero real numbers and are positive constants such that \[\alpha+\beta\leq \gamma+\theta.\] Also, we discuss and illustrate the stability of the solutions of the considered equation via MATLAB at the end of study to support our results.