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

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