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

Turki D. Alharbi; Yacine Halim; Turki D. Alharbi; Yacine Halim

doi:10.3934/math.2025896

AIMS Mathematics

2025, Volume 10, Issue 9: 20050-20065. doi: 10.3934/math.2025896

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

Turki D. Alharbi ¹,
Yacine Halim ^{2,3
,
,}

1.
Department of Mathematics, Al-Leith University College, Umm Al-Qura University, Mecca, 24382, Saudi Arabia
2.
Department of Mathematics, Abdelhafid Boussouf University Center, R.P 26, Mila, 43000, Algeria
3.
LMAM Laboratory, Mohamed Seddik ben Yahia University, BP 78 Oueld Aissa, Jijel, 18000, Algeria

Received: 07 June 2025 Revised: 16 August 2025 Accepted: 25 August 2025 Published: 01 September 2025
MSC : 39A10, 40A05

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.
- system of difference equations,
- local asymptotic stability,
- boundedness,
- oscillation,
- stability
Citation: Turki D. Alharbi, Yacine Halim. Multi-dimensional rational recurrence models: Local analysis with nonlinear effects[J]. AIMS Mathematics, 2025, 10(9): 20050-20065. doi: 10.3934/math.2025896

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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.

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