An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

doi:10.1088/1674-1056/ac7296

中国物理B ›› 2023, Vol. 32 ›› Issue (3): 30203-030203.doi: 10.1088/1674-1056/ac7296

An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

Abderrahmane Abbes^1,†, Adel Ouannas², and Nabil Shawagfeh¹

1 Department of Mathematics, University of Jordan, Amman 11942, Jordan;
2 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria

收稿日期:2022-03-18 修回日期:2022-05-20 接受日期:2022-05-24 出版日期:2023-02-14 发布日期:2023-02-14
通讯作者: Abderrahmane Abbes E-mail:abder.abbes@gmail.com

An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

Abderrahmane Abbes^1,†, Adel Ouannas², and Nabil Shawagfeh¹

1 Department of Mathematics, University of Jordan, Amman 11942, Jordan;
2 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria

Received:2022-03-18 Revised:2022-05-20 Accepted:2022-05-24 Online:2023-02-14 Published:2023-02-14
Contact: Abderrahmane Abbes E-mail:abder.abbes@gmail.com

摘要/Abstract

摘要： This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order. The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically. In particular, the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior. Through using bifurcation diagrams, phase attractors, the maximum Lyapunov exponent and the 0-1 test, we verified that chaos exists in the new model with incommensurate fractional orders. Additionally, a complexity analysis is carried out utilizing the approximation entropy (ApEn) and C₀ complexity to prove that chaos exists. Finally, the main findings of this study are presented using numerical simulations.

关键词: chaos, macroeconomic system, discrete fractional calculus, complexity

Abstract: This study proposes a novel fractional discrete-time macroeconomic system with incommensurate order. The dynamical behavior of the proposed macroeconomic model is investigated analytically and numerically. In particular, the zero equilibrium point stability is investigated to demonstrate that the discrete macroeconomic system exhibits chaotic behavior. Through using bifurcation diagrams, phase attractors, the maximum Lyapunov exponent and the 0-1 test, we verified that chaos exists in the new model with incommensurate fractional orders. Additionally, a complexity analysis is carried out utilizing the approximation entropy (ApEn) and C₀ complexity to prove that chaos exists. Finally, the main findings of this study are presented using numerical simulations.

Key words: chaos, macroeconomic system, discrete fractional calculus, complexity

中图分类号: (Bifurcation theory)

02.30.Oz

02.30.Sa (Functional analysis) 05.45.-a (Nonlinear dynamics and chaos) 05.45.Pq (Numerical simulations of chaotic systems)

Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. 中国物理B, 2023, 32(3): 30203-030203.

Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. Chin. Phys. B, 2023, 32(3): 30203-030203.

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An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity

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