A Qualitative Investigation of the Solution of the Difference Equation $\Psi_{m+1}=\frac{\Psi_{m-3}\Psi_{m-5}}{\Psi_{m-1} \left( \pm1\pm \Psi_{m-3}\Psi_{m-5} \right) }$

Year 2023, Volume: 6 Issue: 2, 78 - 85, 30.06.2023

Burak Oğul , Dağıstan Şimşek , Ibrahim Tarek Fawzi Abdelhamid

https://doi.org/10.33434/cams.1232982

Abstract

We explore the dynamics of adhering to rational difference formula
\begin{equation*}
\Psi_{m+1}=\frac{\Psi_{m-3}\Psi_{m-5}}{\Psi_{m-1} \left( \pm1\pm \Psi_{m-3}\Psi_{m-5} \right) } \quad m \in \mathbb{N}_{0}
\end{equation*}
where the initials $\Psi_{-5}$, $\Psi_{-4}$, $\Psi_{-3}$,$\Psi_{-2}$, $\Psi_{-1}$, $\Psi_{0}$ are arbitrary nonzero real numbers. Specifically, we examine global asymptotically stability. We also give examples and solution diagrams for certain particular instances.

Keywords

Boundedness, Equilibrium point, Global asymptotic stability, Solution of difference equation, Stability

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