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Research Article | Open Access

Multi-dimensional rational recurrence models: Local analysis with nonlinear effects

Turki D. Alharbi1, Yacine Halim2,3( )
Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca, 24382, Saudi Arabia
Department of Mathematics, Abdelhafid Boussouf University Center, R.P 26, Mila, 43000, Algeria
LMAM Laboratory, Mohamed Seddik ben Yahia University, BP 78 Oueld Aissa, Jijel, 18000, Algeria
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Abstract

In this paper, we investigate the dynamic behavior of a class of p-dimensional rational difference equation systems that extend previously studied two- and three-dimensional models. The system incorporates a power-type nonlinearity parameter q > 0, and our analysis focuses on the boundedness of solutions and the local asymptotic stability of equilibrium points. By generalizing known results to higher dimensions, we provide a deeper understanding of the local dynamics and structural properties of such systems.

Keywords

system of difference equationslocal asymptotic stabilityboundednessoscillationstability
CLC number: 39A10, 40A05

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AIMS Mathematics
Volume 10 Issue 9,
September 2025
Pages 20050-20065
DOI: 10.3934/math.2025896

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Alharbi TD, Halim Y. Multi-dimensional rational recurrence models: Local analysis with nonlinear effects. AIMS Mathematics, 2025, 10(9): 20050-20065. https://doi.org/10.3934/math.2025896

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Received: 07 June 2025
Revised: 16 August 2025
Accepted: 25 August 2025
Published: 01 September 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)