Uncovering Exact Solutions in Rational Difference Systems via Algebraic Transformations

Ahmed Ghezal and Najmeddine Attia

Journal of Mathematics, 2026, vol. 2026, 1-14

Abstract: This paper introduces a novel mathematical framework for studying a three-dimensional system of nonlinear difference equations, aimed at describing the discrete-time interactions among three interdependent variables. The proposed approach provides a systematic analytical treatment of the model and reveals its underlying dynamical structure. An innovative algebraic transformation is proposed to reformulate the original system into a factorable bilinear structure, which allows the derivation of explicit closed-form solutions in terms of the initial values and system parameters, without the need for iterative numerical procedures. The obtained solutions are classified according to the nature of the roots of the associated characteristic equation, leading to two distinct cases: repeated roots and distinct roots. Each case exhibits qualitatively different dynamical behaviors, reflecting the influence of the spectral properties of the system. Finally, numerical simulations are presented to illustrate and support the theoretical results, confirming the consistency between analytical derivations and computational behavior.

Date: 2026
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/jmath/2026/5088301.pdf (application/pdf)
http://downloads.hindawi.com/journals/jmath/2026/5088301.xml (application/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:5088301

DOI: 10.1155/jom/5088301

Access Statistics for this article

More articles in Journal of Mathematics from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().