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Stability and bifurcation analysis for the Kaldor–Kalecki model with a discrete delay and a distributed delay

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  • Yu, Jinchen
  • Peng, Mingshu

Abstract

In this paper, a Kaldor–Kalecki model of business cycle with both discrete and distributed delays is considered. With the corresponding characteristic equation analyzed, the local stability of the positive equilibrium is investigated. It is found that there exist Hopf bifurcations when the discrete time delay passes a sequence of critical values. By applying the method of multiple scales, the explicit formulae which determine the direction of Hopf bifurcation and the stability of bifurcating periodic solutions are derived. Finally, numerical simulations are carried out to illustrate our main results.

Suggested Citation

  • Yu, Jinchen & Peng, Mingshu, 2016. "Stability and bifurcation analysis for the Kaldor–Kalecki model with a discrete delay and a distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 66-75.
    • Handle: RePEc:eee:phsmap:v:460:y:2016:i:c:p:66-75
    DOI: 10.1016/j.physa.2016.04.041
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    References listed on IDEAS

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    1. Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.
    2. Pei, Xin & Pan, Yan & Wang, Haixin & Wong, S.C. & Choi, Keechoo, 2016. "Empirical evidence and stability analysis of the linear car-following model with gamma-distributed memory effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 311-323.
    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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    6. Eva Kaslik & Mihaela Neamţu & Loredana Flavia Vesa, 2021. "Global Stability Analysis of a Five-Dimensional Unemployment Model with Distributed Delay," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
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    8. Kaslik, Eva & Kokovics, Emanuel-Attila, 2023. "Stability and bifurcations in scalar differential equations with a general distributed delay," Applied Mathematics and Computation, Elsevier, vol. 454(C).
    9. Kaslik, Eva & Neamţu, Mihaela & Vesa, Loredana Flavia, 2021. "Global stability analysis of an unemployment model with distributed delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 535-546.

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