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Codimension-2 bifurcations of the Kaldor model of business cycle

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  • Wu, Xiaoqin P.

Abstract

In this paper, complete analysis is presented to study codimension-2 bifurcations for the nonlinear Kaldor model of business cycle. Sufficient conditions are given for the model to demonstrate Bautin and Bogdanov–Takens (BT) bifurcations. By computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal forms are derived to obtain the bifurcation diagrams such as Hopf, homoclinic and double limit cycle bifurcations. Some examples are given to confirm the theoretical results.

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  • Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:1:p:28-42
    DOI: 10.1016/j.chaos.2010.11.002
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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. Michal Kalecki, 1937. "A Theory of the Business Cycle," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 77-97.
    3. Varian, Hal R, 1979. "Catastrophe Theory and the Business Cycle," Economic Inquiry, Western Economic Association International, vol. 17(1), pages 14-28, January.
    4. 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.
    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. 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. Irina Bashkirtseva & Davide Radi & Lev Ryashko & Tatyana Ryazanova, 2018. "On the Stochastic Sensitivity and Noise-Induced Transitions of a Kaldor-Type Business Cycle Model," Computational Economics, Springer;Society for Computational Economics, vol. 51(3), pages 699-718, March.
    2. Wenjie Hu & Hua Zhao & Tao Dong, 2018. "Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect," Complexity, Hindawi, vol. 2018, pages 1-11, January.
    3. Riad, Driss & Hattaf, Khalid & Yousfi, Noura, 2016. "Dynamics of a delayed business cycle model with general investment function," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 110-119.
    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. Irina Bashkirtseva & Alexander Pisarchik & Lev Ryashko & Tatyana Ryazanova, 2016. "Excitability And Complex Mixed-Mode Oscillations In Stochastic Business Cycle Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 19(01n02), pages 1-16, February.
    6. Bashkirtseva, Irina & Ryazanova, Tatyana & Ryashko, Lev, 2015. "Analysis of dynamic regimes in stochastically forced Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 96-104.

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