Dynamics and Expressions of Solutions of Fourth-Order Rational Systems of Difference Equations

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DOI: https://doi.org/10.28924/2291-8639-22-2024-163
Published: Sep 26, 2024
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E. M. Elsayed, Q. Din, F. A. Al-Rakhami, N. M. Seyam, Dynamics and Expressions of Solutions of Fourth-Order Rational Systems of Difference Equations, Int. J. Anal. Appl., 22 (2024), 163.

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E. M. Elsayed, Q. Din, F. A. Al-Rakhami, N. M. Seyam

Abstract

The purpose of this article is to determine the expressions of solutions for the following rational difference systems
Φn+1 = Φn−2Ψn / α + Φn−2 + Ψn−3, Ψn+1 = ΦnΨn−2 / β ± Φn−3 ± Ψn−2, n = 0, 1, 2, ...,
where α and β are arbitrary real numbers. Furthermore, the solution’s qualitative behavior is explored, such as local and global stability, as well as the boundedness of the solutions. We will offer numerical examples to demonstrate our results.

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