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

Cited By: 1

https://izlik.org/JA68LY33CN

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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