A Qualitative Investigation of the Solution of the Difference Equation $Psi_{m+1}=frac{Psi_{m-3}Psi_{m-5}}{Psi_{m-1} left( pm1pm Psi_{m-3}Psi_{m-5} right) }$

Authors : Burak Oğul, Dağıstan Şimşek, Ibrahim Tarek Fawzi Abdelhamid

Pages : 78-85

Doi:10.33434/cams.1232982

View : 71 | Download : 30

Publication Date : 2023-06-30

Article Type : Research Paper

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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