Affiliation:
1. ISTANBUL AYDIN UNIVERSITY
2. KONYA TEKNİK ÜNİVERSİTESİ
3. King Khalid University
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.
Publisher
Communications in Advanced Mathematical Sciences
Reference18 articles.
1. [1] R. P. Agarwal, Difference Equations and Inequalities. 1st edition, Marcel Dekker, New York, 1992.
2. [2] V. L. Kocic, G. Ladas, Global behavior of nonlinear difference equations of higher order with applications, volume 256 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1993.
3. [3] M. A. Radin, Difference Equations for Scientists and Engineering, Interdisciplinary Difference Equations, World Scientific Publishing, October 2019.(https://doi.org/10.1142/11349)
4. [4] M. Aloqeili, Dynamics of a rational difference equation, Appl. Math. Comput., 176(2), (2006), 768-774.
5. [5] C. Cinar, On the positive solutions of the difference equation $\Psi_{m+1}=\frac{\Psi_{m-1}}{1+\alpha \Psi_{m} \Psi_{m-1}}$, Appl. Math. Comput., 158(3), (2004), 809-812.