Work

On Variable-Order Fractional Discrete Macroeconomic Model: Stability, Chaos, and Complexity

Year: 2025

Type: article

Abstract: Macroeconomic mathematical models are practical instruments structured to carry out theoretical analyses of macroeconomic developments. In this manuscript, the Caputo-like fractional operator of variable order is used to introduce and investigate the mechanism of the discrete macroeconomic model. The nature of the dynamics was established, and the emergence of chaos using a distinct variable fractional order, especially the stability of the trivial solution, is examined. The findings reveal that the variable-order discrete macroeconomic model displays chaotic dynamics employing bifurcation, the Largest Lyapunov exponent (LEmax), the phase portraits, and the 0–1 test. Furthermore, a complexity analysis is performed to demonstrate the existence of chaos and quantify its complexity using C0 complexity and spectral entropy (SE). These studies show that the suggested variable-order fractional discrete macroeconomic model has more complex features than integer and constant fractional orders. Finally, MATLAB R2024b simulations are run to exemplify the outcomes of this study.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9110723

Authors: Ali Aloui, Louiza Diabi, Omar Kahouli, Adel Ouannas, Lilia El Amraoui, Mohamed Ayari

Institutions: University of Ha'il, Larbi Ben M'hidi University of Oum El Bouaghi, Princess Nourah bint Abdulrahman University, Northern Border University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: Princess Nourah Bint Abdulrahman University, Northern Border University