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Dynamic Analysis for a Kaldor–Kalecki Model of Business Cycle with Time Delay and Diffusion Effect

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  • Wenjie Hu
  • Hua Zhao
  • Tao Dong

Abstract

The dynamics behaviors of Kaldor–Kalecki business cycle model with diffusion effect and time delay under the Neumann boundary conditions are investigated. First the conditions of time-independent and time-dependent stability are investigated. Then, we find that the time delay can give rise to the Hopf bifurcation when the time delay passes a critical value. Moreover, the normal form of Hopf bifurcations is obtained by using the center manifold theorem and normal form theory of the partial differential equation, which can determine the bifurcation direction and the stability of the periodic solutions. Finally, numerical results not only validate the obtained theorems, but also show that the diffusion coefficients play a key role in the spatial pattern. With the diffusion coefficients increasing, different patterns appear.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:complx:1263602
    DOI: 10.1155/2018/1263602
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    References listed on IDEAS

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    1. 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.
    2. Saijo, Hikaru, 2017. "The uncertainty multiplier and business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 1-25.
    3. 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.
    4. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor model," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2462-2468.
    5. Cox, Raymond A.K. & Dayanandan, Ajit & Donker, Han & Nofsinger, John, 2017. "The Bad, the boom and the bust: Profit warnings over the business cycle," Journal of Economics and Business, Elsevier, vol. 89(C), pages 13-19.
    6. 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.
    7. Wu, Xiaoqin P., 2011. "Codimension-2 bifurcations of the Kaldor model of business cycle," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 28-42.
    8. R. Rajaram & B. Castellani & A. N. Wilson, 2017. "Advancing Shannon Entropy for Measuring Diversity in Systems," Complexity, Hindawi, vol. 2017, pages 1-10, May.
    9. Dobrescu, Loretti I. & Opris, Dumitru, 2009. "Neimark–Sacker bifurcation for the discrete-delay Kaldor–Kalecki model," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2405-2413.
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    Cited by:

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