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Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model

Author

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  • Chu, Yu-Ming
  • Bekiros, Stelios
  • Zambrano-Serrano, Ernesto
  • Orozco-López, Onofre
  • Lahmiri, Salim
  • Jahanshahi, Hadi
  • Aly, Ayman A.

Abstract

In this novel research, through dynamical analysis, we introduce for the first time a fractional-calculus based artificial macroeconomic model, actually implemented in the Laboratory via a new hardware set up. Firstly, we propose a new model of a discrete-time macroeconomic system where fractional derivatives are incorporated into the system of equations. Using well-known tools and methods, including bifurcation diagrams and Lyapunov exponents, the characteristics of the system are disclosed, and the importance of the fractional-order derivative in the modeling of the system is shown. After that, a laboratory hardware realization is also carried out for the proposed system that provides further insight and a better understanding of the properties of the system. For the hardware realization an Arduino Due™ is chosen in which possess two analog output pins. Experimental results conspicuously illustrate the chaotic behavior of the system. Through the results of the hardware realization, phase portraits and bifurcation diagram of the system are demonstrated, and the effects of the parameters and fractional derivatives are studied. We believe the presented study and its results pave the way for future studies on the incorporation of fractional calculus into macroeconomic models.

Suggested Citation

  • Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001284
    DOI: 10.1016/j.chaos.2021.110776
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    1. Volker Wieland & Maik Wolters, 2011. "The diversity of forecasts from macroeconomic models of the US economy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(2), pages 247-292, June.
    2. A G Haldane & A E Turrell, 2018. "An interdisciplinary model for macroeconomics," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 34(1-2), pages 219-251.
    3. Tarasov, Vasily E. & Tarasova, Valentina V., 2018. "Macroeconomic models with long dynamic memory: Fractional calculus approach," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 466-486.
    4. Wieland, Volker & Cwik, Tobias & Müller, Gernot J. & Schmidt, Sebastian & Wolters, Maik, 2012. "A new comparative approach to macroeconomic modeling and policy analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 83(3), pages 523-541.
    5. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    6. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    7. Puu, Tonu, 1986. "Multiplier-accelerator models revisited," Regional Science and Urban Economics, Elsevier, vol. 16(1), pages 81-95, February.
    8. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    9. Wang, Shaojie & He, Shaobo & Yousefpour, Amin & Jahanshahi, Hadi & Repnik, Robert & Perc, Matjaž, 2020. "Chaos and complexity in a fractional-order financial system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    10. Masson, Paul, 1999. "Contagion:: macroeconomic models with multiple equilibria," Journal of International Money and Finance, Elsevier, vol. 18(4), pages 587-602, August.
    11. Fontana, Giuseppe & Veronese Passarella, Marco, 2020. "Unconventional monetary policies from conventional theories: Modern lessons for central bankers," Journal of Policy Modeling, Elsevier, vol. 42(3), pages 503-519.
    12. Olivier Blanchard, 2018. "On the future of macroeconomic models," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 34(1-2), pages 43-54.
    13. Huang, Chengdai & Cao, Jinde, 2017. "Active control strategy for synchronization and anti-synchronization of a fractional chaotic financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 262-275.
    14. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    15. Yousefpour, Amin & Jahanshahi, Hadi & Bekiros, Stelios, 2020. "Optimal policies for control of the novel coronavirus disease (COVID-19) outbreak," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    16. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    17. Wang, Shaojie & Bekiros, Stelios & Yousefpour, Amin & He, Shaobo & Castillo, Oscar & Jahanshahi, Hadi, 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    18. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    19. Chen, Shu-Bo & Jahanshahi, Hadi & Alhadji Abba, Oumate & Solís-Pérez, J.E. & Bekiros, Stelios & Gómez-Aguilar, J.F. & Yousefpour, Amin & Chu, Yu-Ming, 2020. "The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    20. O.Y. Voronkova & А.M. Zadimidcenko & L.V. Goloshchapova & A.G. Polyakova & S.G. Kamolov & E.M. Akhmetshin, 2018. "Economic and Mathematical Modeling of Regional Industrial Processes," European Research Studies Journal, European Research Studies Journal, vol. 0(4), pages 268-279.
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    4. Qing Ding & Oumate Alhadji Abba & Hadi Jahanshahi & Madini O. Alassafi & Wen-Hua Huang, 2022. "Dynamical Investigation, Electronic Circuit Realization and Emulation of a Fractional-Order Chaotic Three-Echelon Supply Chain System," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    5. Wang, Bo & Liu, Jinping & Alassafi, Madini O. & Alsaadi, Fawaz E. & Jahanshahi, Hadi & Bekiros, Stelios, 2022. "Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    6. Bekiros, Stelios & Yao, Qijia & Mou, Jun & Alkhateeb, Abdulhameed F. & Jahanshahi, Hadi, 2023. "Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    7. Zhenggang Guo & Junjie Wen & Jun Mou, 2022. "Dynamic Analysis and DSP Implementation of Memristor Chaotic Systems with Multiple Forms of Hidden Attractors," Mathematics, MDPI, vol. 11(1), pages 1-13, December.
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