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Complex dynamics of a Kaldor model of business cycle with discrete-time

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  • Eskandari, Z.
  • Avazzadeh, Z.
  • Khoshsiar Ghaziani, R.

Abstract

This paper studies the dynamical behavior of a Kaldor model of business cycle with discrete-time analytically and numerically. The conditions and the critical coefficients for the flip (period-doubling), Neimark-Sacker, and strong resonances are computed analytically. By using the critical coefficients, the bifurcation scenarios are determined for each of the deleted bifurcation points. Bifurcation curves of fixed points and cycles with periods up to sixteen by changing one and two parameters along with all codim-1 and codim-2 bifurcations on the corresponding curves are computed using the numerical continuation method. Numerical analysis confirms our analytical results and reveals more complex dynamical behaviors.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s0960077922000741
    DOI: 10.1016/j.chaos.2022.111863
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    References listed on IDEAS

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    1. Pecora, Nicolò, 2018. "Analysis of 1:4 resonance in a monopoly model with memory," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 95-104.
    2. Toichiro Asada & Christos Douskos & Panagiotis Markellos, 2007. "Numerical Exploration of Kaldorian Macrodynamics: Hopf-Neimark Bifurcations and Business Cycles with Fixed Exchange Rates," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-16, April.
    3. Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
    4. W. W. Chang & D. J. Smyth, 1971. "The Existence and Persistence of Cycles in a Non-linear Model: Kaldor's 1940 Model Re-examined," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 37-44.
    5. Grasman, Johan & Wentzel, Jolanda J., 1994. "Co-existence of a limit cycle and an equilibrium in Kaldor's business cycle model and its consequences," Journal of Economic Behavior & Organization, Elsevier, vol. 24(3), pages 369-377, August.
    6. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    7. 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).
    8. Toichiro Asada & Christos Douskos & Panagiotis Markellos, 2008. "Numerical Exploration of Kaldorian Macrodynamics: Enhanced Stability and Predominance of Period Doubling and Chaos with Flexible Exchange Rates," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-23, September.
    9. Agliari, Anna & Dieci, Roberto & Gardini, Laura, 2007. "Homoclinic tangles in a Kaldor-like business cycle model," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 324-347, March.
    10. A. Krawiec & M. Szydlowski, 1999. "The Kaldor‐Kalecki business cycle model," Annals of Operations Research, Springer, vol. 89(0), pages 89-100, January.
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