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An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity |
| Abderrahmane Abbes1,†, 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 |
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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.
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Received: 18 March 2022
Revised: 20 May 2022
Accepted manuscript online: 24 May 2022
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PACS:
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02.30.Oz
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(Bifurcation theory)
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02.30.Sa
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(Functional analysis)
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05.45.-a
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(Nonlinear dynamics and chaos)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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Corresponding Authors:
Abderrahmane Abbes
E-mail: abder.abbes@gmail.com
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Cite this article:
Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity 2023 Chin. Phys. B 32 030203
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