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Research Article | Open Access

On the global behavior and the periodicity of the solutions of a k-dimensional system of difference equations

Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia; mesmoulimouataz@hotmail.com, mo.abdelkader@uoh.edu.sa, tshassan@mans.edu.eg
LMAM Laboratory, Faculty of Exact Sciences and Informatics, University of Jijel, Jijel 18000, Algeria
Department of Computing, Mathematics and Electronics, 1 Decembrie 1918 University of Alba Iulia, 510009 Alba Iulia, Romania; lucian.popa@uab.ro
Faculty of Mathematics and Computer Science, Transilvania University of Brasov, Iuliu Maniu Street 50, 500091 Brasov, Romania
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Abstract

In this work, we provide a detailed study on the behavior of solutions of a k-dimensional system of rational difference equations, extending some existing results in the literature. We use the linearized stability theory to establish conditions for the local stability of the corresponding unique equilibrium point, and to show its global stability, we prove that the equilibrium point is a global attractor. Also, conditions for the existence of periodic solutions are provided. Our obtained results are confirmed by some examples.

Keywords

system of difference equationsequilibrium pointsstabilityboundednessperiodicity
CLC number: 39A05, 39A23, 39A30

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AIMS Mathematics
Volume 10 Issue 8,
August 2025
Pages 17940-17953
DOI: 10.3934/math.2025799

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Mesmouli MB, Touafek N, Popa I-L, et al. On the global behavior and the periodicity of the solutions of a k-dimensional system of difference equations. AIMS Mathematics, 2025, 10(8): 17940-17953. https://doi.org/10.3934/math.2025799

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Received: 03 May 2025
Revised: 03 June 2025
Accepted: 17 June 2025
Published: 15 August 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)