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Generic and symmetric bifurcations analysis of a three dimensional economic model

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  • Alidousti, J.
  • Eskandari, Z.
  • Avazzadeh, Z.

Abstract

This paper studies bifurcation analysis of an economic model by using the critical normal form coefficients method which is one of the most influential methods in bifurcation theory. This method advantageously checks the non-degeneracy condition without computing the central manifold and converting the linear part of the map into Jordan form. In this study, the codimension one and codimension two bifurcations of the model are investigated by considering different parameters and for each bifurcation, the normal form coefficients are computed. The obtained results conclude that the model undergoes bifurcations such as flip (period-doubling), Neimark-Sacker, resonance 1:3, resonance 1:4, Chenciner and period-doubling Neimark-Sacker. Furthermore, to accomplish symmetric bifurcation analysis of the model, the normal form of the Z3-symmetric double-1 multiplier bifurcation is utilized. The bifurcation curves of the model are drawn with the aid of the numerical continuation method. From the mathematical point of view, these bifurcation curves and numerical simulations not only support the theoretical results but also reveal more details of the dynamic system under study, especially after higher iterations. The achieved results directly can be applied to design and optimize many types of economic models.

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  • Alidousti, J. & Eskandari, Z. & Avazzadeh, Z., 2020. "Generic and symmetric bifurcations analysis of a three dimensional economic model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306470
    DOI: 10.1016/j.chaos.2020.110251
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    References listed on IDEAS

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    1. Čermák, Jan & Nechvátal, Luděk, 2019. "Stability and chaos in the fractional Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 24-33.
    2. Al-khedhairi, A. & Matouk, A.E. & Khan, I., 2019. "Chaotic dynamics and chaos control for the fractional-order geomagnetic field model," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 390-401.
    3. Bischi, Gian Italo & Gardini, Laura & Kopel, Michael, 2000. "Analysis of global bifurcations in a market share attraction model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 855-879, June.
    4. Liu, Xiaoli & Xiao, Dongmei, 2007. "Complex dynamic behaviors of a discrete-time predator–prey system," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 80-94.
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    Cited by:

    1. Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Yao, Xiao-Yue & Li, Xian-Feng & Jiang, Jun & Leung, Andrew Y.T., 2022. "Codimension-one and -two bifurcation analysis of a two-dimensional coupled logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    4. Eskandari, Z. & Avazzadeh, Z. & Khoshsiar Ghaziani, R., 2022. "Complex dynamics of a Kaldor model of business cycle with discrete-time," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Sorin Lugojan & Loredana Ciurdariu & Eugenia Grecu, 2022. "Another Case of Degenerated Discrete Chenciner Dynamic System and Economics," Mathematics, MDPI, vol. 10(20), pages 1-19, October.

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