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Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis

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  • Bazán Navarro, Ciro Eduardo
  • Benazic Tomé, Renato Mario

Abstract

In this article, we analyze the conditions for the structural stability of a fractional order IS-LM-AS dynamic model with adaptive expectations. It is a generalization of our previous research lately published in the literature. We also present the conditions that the structural parameters of the model must meet for the economic system to present a periodic movement when the critical value of the fractional order of the system, q* , guarantees the presence of a Hopf bifurcation of degenerate type. The theoretical analysis is complemented with numerical simulations of the phase portraits in R3 and of the temporal trajectories of the solutions of the model in MATLAB software. Finally, it is important to highlight that unlike the results of our previous research, the qualitative results found in this paper show that all the structural parameters of the model are essential in determining its global asymptotic stability and Hopf bifurcation.

Suggested Citation

  • Bazán Navarro, Ciro Eduardo & Benazic Tomé, Renato Mario, 2024. "Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 425-443.
    • Handle: RePEc:eee:matcom:v:217:y:2024:i:c:p:425-443
    DOI: 10.1016/j.matcom.2023.11.003
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    1. Zhiqin Qiao & Xianyi Li, 2014. "Dynamical analysis and numerical simulation of a new Lorenz-type chaotic system," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 20(3), pages 264-283, May.
    2. Caputo Michele, 2012. "The Convergence of Economic Developments," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-23, April.
    3. 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.
    4. 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).
    5. Lin, Zifei & Li, Jiaorui & Li, Shuang, 2016. "On a business cycle model with fractional derivative under narrow-band random excitation," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 61-70.
    6. Sasakura, Kazuyuki, 1994. "On the dynamic behavior of Schinasi's business cycle model," Journal of Macroeconomics, Elsevier, vol. 16(3), pages 423-444.
    7. José M. Gaspar, 2018. "Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab," Journal of Applied Mathematics, Hindawi, vol. 2018, pages 1-13, January.
    8. Paul Yaovi Dousseh & Cyrille Ainamon & Clément Hodévèwan Miwadinou & Adjimon Vincent Monwanou & Jean Bio Chabi Orou & Guillermo Huerta Cuellar, 2021. "Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode," Complexity, Hindawi, vol. 2021, pages 1-15, July.
    9. Ciro Eduardo Bazán Navarro & Renato Mario Benazic Tomé & Peiguang Wang, 2022. "Structural Stability Analysis in a Dynamic IS-LM-AS Macroeconomic Model with Inflation Expectations," International Journal of Differential Equations, Hindawi, vol. 2022, pages 1-21, October.
    10. Mamadou Diouf & Ndolane Sene, 2020. "Analysis of the Financial Chaotic Model with the Fractional Derivative Operator," Complexity, Hindawi, vol. 2020, pages 1-14, June.
    11. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    12. Chengdai Huang & Heng Liu & Yuefen Chen & Xiaoping Chen & Fang Song, 2021. "Dynamics Of A Fractional-Order Bam Neural Network With Leakage Delay And Communication Delay," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-14, May.
    13. 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.
    14. Wen, Chunhui & Yang, Jinhai, 2019. "Complexity evolution of chaotic financial systems based on fractional calculus," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 242-251.
    15. Fuchen Zhang & Gaoxiang Yang & Yong Zhang & Xiaofeng Liao & Guangyun Zhang, 2018. "Qualitative Study of a 4D Chaos Financial System," Complexity, Hindawi, vol. 2018, pages 1-5, July.
    16. Yiding Yue & Lei He & Guanchun Liu, 2013. "Modeling and Application of a New Nonlinear Fractional Financial Model," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, November.
    17. Song, Jingjing, 2020. "Research on fast numerical calculation based on fractional calculus model for macroeconomic growth," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    18. Yi Liao & Yiran Zhou & Fei Xu & Xiao-Bao Shu, 2020. "A Study on the Complexity of a New Chaotic Financial System," Complexity, Hindawi, vol. 2020, pages 1-5, October.
    19. Torre, V, 1977. "Existence of Limit Cycles and Control in Complete Keynesian System by Theory of Bifurcations," Econometrica, Econometric Society, vol. 45(6), pages 1457-1466, September.
    20. Schinasi, Garry J., 1982. "Fluctuations in a dynamic, intermediate-run IS-LM model: Applications of the Poincare-Bendixon theorem," Journal of Economic Theory, Elsevier, vol. 28(2), pages 369-375, December.
    21. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    22. Turnovsky, Stephen J., 2008. "The role of factor substitution in the theory of economic growth and income distribution: Two examples," Journal of Macroeconomics, Elsevier, vol. 30(2), pages 604-629, June.
    23. Vasily E. Tarasov, 2020. "Non-Linear Macroeconomic Models of Growth with Memory," Mathematics, MDPI, vol. 8(11), pages 1-22, November.
    24. Acay, Bahar & Bas, Erdal & Abdeljawad, Thabet, 2020. "Fractional economic models based on market equilibrium in the frame of different type kernels," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    25. Paul Yaovi Dousseh & Cyrille Ainamon & Clément Hodévèwan Miwadinou & Adjimon Vincent Monwanou & Jean Bio Chabi Orou, 2021. "Corrigendum to “Chaos in a Financial System with Fractional Order and Its Control via Sliding Modeâ€," Complexity, Hindawi, vol. 2021, pages 1-16, November.
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