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E. M. Elsayed, J. G. Al-Juaid, H. Malaikah, On the dynamical behaviors of a quadratic difference equation of order three, Eur. J. Math. Appl. 3 (2023), Article ID 1.

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Volume 3 (2023), Article ID 1

https://doi.org/10.28919/ejma.2023.3.1

Published: 13/01/2023

Abstract:

In this paper provides proof of the existence of periodicity, asymptotic behavior, and boundedness of the following quadratic three order difference equation
\begin{equation*}
w_{n+1}=\zeta w_{n-1} +\frac{\eta w_{n-1}^{2}+\rho w_{n-1} w_{n-2}+\kappa w_{n-2}^{2}}{\alpha w_{n-1}^{2}+\beta w_{n-1}w_{n-2}+\gamma w_{n-2}^{2}}, n=0,1,2,\dots ,
\end{equation*}
constants $ \zeta, \eta, \rho, \kappa, \alpha, \beta $ and $\gamma$ are positive real numbers and the initial conditions $ w_{-2},w_{-1}$ and $w_{0}$ are arbitrary non zero real numbers.

How to Cite:

E. M. Elsayed, J. G. Al-Juaid, H. Malaikah, On the dynamical behaviors of a quadratic difference equation of order three, Eur. J. Math. Appl. 3 (2023), Article ID 1. https://doi.org/10.28919/ejma.2023.3.1