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Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays

Author

Listed:
  • Yanhui Zhai
  • Ying Xiong
  • Xiaona Ma

Abstract

The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid.

Suggested Citation

  • Yanhui Zhai & Ying Xiong & Xiaona Ma, 2014. "Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:686274
    DOI: 10.1155/2014/686274
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    References listed on IDEAS

    as
    1. Adeyemi, Olutomi I. & Hunt, Lester C., 2007. "Modelling OECD industrial energy demand: Asymmetric price responses and energy-saving technical change," Energy Economics, Elsevier, vol. 29(4), pages 693-709, July.
    2. Yanhui Zhai & Haiyun Bai & Ying Xiong & Xiaona Ma, 2013. "Hopf Bifurcation Analysis for the Modified Rayleigh Price Model with Time Delay," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Yanhui Zhai & Haiyun Bai & Ying Xiong & Xiaona Ma, 2013. "Hopf Bifurcation Analysis for the Modified Rayleigh Price Model with Time Delay," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, August.
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