Stability of the third order rational difference equation

Year 2020, Volume: 8 Issue: 1, 68 - 76, 30.06.2020

Mehmet Emre Erdoğan

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.

Keywords

Asymptotic Stability, Difference Equation, Global Behavior

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