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

Hashem Althagafi () and Ahmed Ghezal
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Hashem Althagafi: Mathematics Department, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia
Ahmed Ghezal: Department of Mathematics, University Center of Mila, Mila 43000, Algeria

Mathematics, 2024, vol. 12, issue 8, 1-20

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.

Keywords: system of difference equations; local stability; Fibonacci sequence; equilibrium point and nonlinear difference equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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