IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v142y2021ics0960077920307724.html
   My bibliography  Save this article

Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control

Author

Listed:
  • Zhou, Shuang-Shuang
  • Jahanshahi, Hadi
  • Din, Qamar
  • Bekiros, Stelios
  • Alcaraz, Raúl
  • Alassafi, Madini O.
  • Alsaadi, Fawaz E.
  • Chu, Yu-Ming

Abstract

Economic systems, due to their substantial effects on any society, are interesting research subject for a large family of researchers. Despite all attempts to study economic and financial systems, studies on discrete-time macroeconomic systems are rare. Hence, in the current study, we aim to investigate dynamical behavior and synchronization of these systems. At first, the discrete-time mathematical model of the macroeconomic system is presented. Then, the system is studied through topological classification, bifurcation analysis, Lyapunov exponents, and manifold theory, which are powerful tools in the investigation of nonlinear systems. This way, the features of the system are disclosed, and the existence of chaos in the system is shown. For the adequate performance of the economy, the economic systems are desired to operate in a unified manner. To this end, in the present research, a fuzzy based-activation feedback controller is proposed for the synchronization of the system. To enhance the celerity and accuracy of the proposed control for synchronization purposes, it is equipped with a fuzzy logic engine. Finally, the numerical simulations of the synchronization are presented and compared with those of a conventional activation feedback control. Numerical results verify that the proposed control technique can successfully push the states of the response system to the desired value.

Suggested Citation

  • Zhou, Shuang-Shuang & Jahanshahi, Hadi & Din, Qamar & Bekiros, Stelios & Alcaraz, Raúl & Alassafi, Madini O. & Alsaadi, Fawaz E. & Chu, Yu-Ming, 2021. "Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307724
    DOI: 10.1016/j.chaos.2020.110378
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920307724
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110378?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Jean Imbs, 2004. "Trade, Finance, Specialization, and Synchronization," The Review of Economics and Statistics, MIT Press, vol. 86(3), pages 723-734, August.
    3. 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).
    4. Aguiar-Conraria, LuI´s & Joana Soares, Maria, 2011. "Business cycle synchronization and the Euro: A wavelet analysis," Journal of Macroeconomics, Elsevier, vol. 33(3), pages 477-489, September.
    5. M. Ayhan Kose & Eswar S. Prasad & Marco E. Terrones, 2003. "How Does Globalization Affect the Synchronization of Business Cycles?," American Economic Review, American Economic Association, vol. 93(2), pages 57-62, May.
    6. 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.
    7. 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.
    8. Park, Ju H., 2005. "Chaos synchronization of a chaotic system via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 579-584.
    9. Kaas, Leo, 1998. "Stabilizing chaos in a dynamic macroeconomic model," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 313-332, January.
    10. 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).
    11. David Kendrick, 1976. "Applications of Control Theory to Macroeconomics," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 2, pages 171-190, National Bureau of Economic Research, Inc.
    12. 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).
    13. 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).
    14. Andreas Groth & Michael Ghil, 2017. "Synchronization of world economic activity," Post-Print hal-01701086, HAL.
    15. 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).
    16. 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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhu, Wanting & Sun, Kehui & He, Shaobo & Wang, Huihai & Liu, Wenhao, 2023. "A class of m-dimension grid multi-cavity hyperchaotic maps and its application," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. 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.
    3. 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).
    4. 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).
    5. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    7. Alsaade, Fawaz W. & Yao, Qijia & Bekiros, Stelios & Al-zahrani, Mohammed S. & Alzahrani, Ali S. & Jahanshahi, Hadi, 2022. "Chaotic attitude synchronization and anti-synchronization of master-slave satellites using a robust fixed-time adaptive controller," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Jahanshahi, Hadi & Sajjadi, Samaneh Sadat & Bekiros, Stelios & Aly, Ayman A., 2021. "On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    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. 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).
    7. Xiong, Pei-Ying & Jahanshahi, Hadi & Alcaraz, Raúl & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alsaadi, Fawaz E., 2021. "Spectral Entropy Analysis and Synchronization of a Multi-Stable Fractional-Order Chaotic System using a Novel Neural Network-Based Chattering-Free Sliding Mode Technique," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    8. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    9. Wang, Yong-Long & Jahanshahi, Hadi & Bekiros, Stelios & Bezzina, Frank & Chu, Yu-Ming & Aly, Ayman A., 2021. "Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Bambe Moutsinga, Claude Rodrigue & Pindza, Edson & Maré, Eben, 2021. "Comparative performance of time spectral methods for solving hyperchaotic finance and cryptocurrency systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    11. Bekiros, Stelios & Jahanshahi, Hadi & Bezzina, Frank & Aly, Ayman A., 2021. "A novel fuzzy mixed H2/H∞ optimal controller for hyperchaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    12. Bekiros, Stelios & Laarem, Guessas & Mou, Jun & Al-Barakati, Abdullah A. & Jahanshahi, Hadi, 2023. "Heterogeneous agent-based modeling of endogenous boom-bust cycles in financial markets with adaptive expectations and dynamically switching fractions between contrarian and fundamental market entry st," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    13. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    14. Alsaadi, Fawaz E. & Bekiros, Stelios & Yao, Qijia & Liu, Jinping & Jahanshahi, Hadi, 2023. "Achieving resilient chaos suppression and synchronization of fractional-order supply chains with fault-tolerant control," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    15. 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).
    16. Fawaz E. Alsaadi & Amirreza Yasami & Christos Volos & Stelios Bekiros & Hadi Jahanshahi, 2023. "A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    17. 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).
    18. Dima, Bogdan & Dima, Ştefana Maria, 2017. "Energy consumption synchronization between Europe, United States and Japan: A spectral analysis assessment," Renewable and Sustainable Energy Reviews, Elsevier, vol. 77(C), pages 1261-1271.
    19. Erden, Lutfi & Ozkan, Ibrahim, 2014. "Determinants of international transmission of business cycles to Turkish economy," Economic Modelling, Elsevier, vol. 36(C), pages 383-390.
    20. Razieh Zahedi & Asghar Shahmoradi & Ali Taiebnia, 2022. "The ever-evolving trade pattern: a global VAR approach," Empirical Economics, Springer, vol. 63(3), pages 1193-1218, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307724. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.