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Dynamics of a delayed business cycle model with general investment function

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  • Riad, Driss
  • Hattaf, Khalid
  • Yousfi, Noura

Abstract

The aim of this paper is to study the dynamics of a delayed business cycle model with general investment function. The model describes the interaction of the gross product and capital stock. Furthermore, the delay represents the time between the decision of investment and implementation. Firstly, we show that the model is well posed by proving the global existence and boundedness of solutions. Secondly, we determine the economic equilibrium of the model. By analyzing the characteristic equation, we investigate the stability of the economic equilibrium and the local existence of Hopf bifurcation. Also, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory. Moreover, the global existence of bifurcating periodic solutions is established by using the global Hopf bifurcation theory. Finally, our theoretical results are illustrated with some numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:85:y:2016:i:c:p:110-119
    DOI: 10.1016/j.chaos.2016.01.022
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    References listed on IDEAS

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    1. Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
    2. 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. 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.
    2. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    3. Hattaf, Khalid & Riad, Driss & Yousfi, Noura, 2017. "A generalized business cycle model with delays in gross product and capital stock," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 31-37.

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