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Journal of Applied Nonlinear Dynamics 10(4) (2021) 709--719 | DOI:10.5890/JAND.2021.12.010

M. B. Almatrafi$^1$ , Marwa M. Alzubaidi$^2$

$^1$ Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

$^2$ Department of Mathematics, College of Duba, University of Tabuk, Saudia Arabia

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Abstract

Nonlinear difference equations are mostly utilized to describe some natural phenomena. The exact solutions of some models cannot be sometimes extracted. Therefore, investigating the long behaviour of the model may give the future pattern of the respective problem. This article manifests the long behaviour of a seventh order rational difference equation with positive real coefficients. Through this paper, the local stability, global stability, boundedness are obtained analytically and some figures are illustrated to test the accuracy of the solutions. The used technique can be extended to be utilized in solving some higher order difference equations.

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