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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:

    1. Yüksel, Mustafa Kerem, 2011. "Capital dependent population growth induces cycles," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 759-763.
    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. 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.
    4. 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.
    5. 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.
    6. Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
    7. Akio Matsumoto & Ferenc Szidarovszky, 2024. "Nonlinear Kaldor model augmented with retardation and anticipation," Annals of Operations Research, Springer, vol. 337(3), pages 937-958, June.
    8. 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.
    9. Willi Semmler & Fabio Della Rossa & Giuseppe Orlando & Gabriel R. Padro Rosario & Levent Kockesen, 2023. "Endogenous Economic Resilience, Loss of Resilience, Persistent Cycles, Multiple Attractors, and Disruptive Contractions," Working Papers 2309, New School for Social Research, Department of Economics.

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