Behavior and Solution Representations of Fourth-Order Rational Systems of Difference Equations

Authors

  • Hanan S. Gafel Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia.
  • Haya Altamimi Department of Mathematics and Statistics, College of Science, Taif University, Taif 21944, Saudi Arabia.

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i3.6218

Keywords:

Difference equations, Fourth-Order, Rational Systems, local and global stability

Abstract

Our aim in this paper is to obtain formulas expressions for solutions of the difference equations. The purpose of this article is to determine the expressions of solutions for the following rational difference systems
\[
\Theta_{n+1} = \frac{\Theta_{n-2} \Omega_n}{\alpha \pm \Theta_{n-2} \pm \Omega_{n-3}}, \quad 
\Omega_{n+1} = \frac{\Theta_n \Omega_{n-2}}{\beta + \Theta_{n-3} + \Omega_{n-2}}, \quad n = 0, 1, 2, \ldots
\]
where the real numbers $\alpha$ and $\beta$ are arbitrary. Additionally, the qualitative behavior of the solutions is analyzed, including their boundedness as well as their local and global stability. We will illustrate our findings with numerical examples.

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Published

2025-08-01

Issue

Vol. 18 No. 3: (July 2025)

Section

Partial Differential Equations and Dynamical Systems

License

Copyright (c) 2025 Hanan S. Gafel, Haya Altamimi

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How to Cite

Behavior and Solution Representations of Fourth-Order Rational Systems of Difference Equations. (2025). European Journal of Pure and Applied Mathematics, 18(3), 6218. https://doi.org/10.29020/nybg.ejpam.v18i3.6218