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The stability problem in the Kaldor–Kalecki business cycle model

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  • Szydłowski, Marek
  • Krawiec, Adam

Abstract

We consider the Kaldor–Kalecki model of the business cycle which is the modified Kaldor model with the Kalecki time delay in investment. The model is formulated in terms of a second-order nonlinear delay differential equation with a negative feedback. We investigate the problem of stability of cycles caused by retarded action. The method of a centre manifold is used to find the conditions for the Hopf bifurcation. The conditions for stability of limit cycles on the centre manifold is given.

Suggested Citation

  • Szydłowski, Marek & Krawiec, Adam, 2005. "The stability problem in the Kaldor–Kalecki business cycle model," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 299-305.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:2:p:299-305
    DOI: 10.1016/j.chaos.2004.11.012
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    References listed on IDEAS

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    1. 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.
    2. Mullineux, Andy & Peng, WenSheng, 1993. "Nonlinear Business Cycle Modelling," Journal of Economic Surveys, Wiley Blackwell, vol. 7(1), pages 41-83.
    3. 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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    Cited by:

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    2. Neamţu, Mihaela & Opriş, Dumitru & Chilaˇrescu, Constantin, 2007. "Hopf bifurcation in a dynamic IS–LM model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 519-530.
    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. Januário, Cristina & Grácio, Clara & Duarte, Jorge, 2009. "Measuring complexity in a business cycle model of the Kaldor type," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2890-2903.
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    6. Li, Wei & Xu, Wei & Zhao, Junfeng & Jin, Yanfei, 2007. "Stochastic stability and bifurcation in a macroeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 702-711.
    7. Brianzoni, Serena & Mammana, Cristiana & Michetti, Elisabetta, 2009. "Nonlinear dynamics in a business-cycle model with logistic population growth," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 717-730.
    8. De Cesare, Luigi & Sportelli, Mario, 2022. "A non-linear approach to Kalecki’s investment cycle," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 57-70.

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