Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations-Reference-Cited by-同舟云学术

Analytical Study of Nonlinear Systems of Higher-Order Difference Equations: Solutions, Stability, and Numerical Simulations

Published:2024-04-12 Issue:8 Volume:12 Page:1159
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Althagafi Hashem¹,Ghezal Ahmed²

Affiliation:

1. Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia

2. Department of Mathematics, University Center of Mila, Mila 43000, Algeria

Abstract

This paper aims to derive analytical expressions for solutions of fractional bidimensional systems of difference equations with higher-order terms under specific parametric conditions. Additionally, formulations of solutions for one-dimensional equations derived from these systems are explored. Furthermore, rigorous proof is provided for the local stability of the unique positive equilibrium point of the proposed systems. The theoretical findings are validated through numerical examples using MATLAB, facilitating graphical illustrations of the results.

Publisher

MDPI AG

Link

https://www.mdpi.com/2227-7390/12/8/1159/pdf

Reference19 articles.

1. On Markov-switching asymmetric logGARCH models: Stationarity and estimation;Ghezal;Filomat,2023

2. Ghezal, A. (2023). Spectral representation of Markov-switching bilinear processes. São Paulo J. Math. Sci., 1–21.

3. Dynamical analysis of a discrete-time COVID-19 epidemic model;Khan;Math. Meth. Appl. Sci.,2022

4. Khaliq, A., Mustafa, I., Ibrahim, T.F., Osman, W.M., Al-Sinan, B.R., Dawood, A.A., and Juma, M.Y. (2023). Stability and bifurcation analysis of fifth-order nonlinear fractional difference equation. Fractal Fract., 7.

5. On the dynamics of a discrete fractional-order cournot–bertrand competition duopoly game;Elsadany;Math. Probl. Eng.,2022