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Dynamics Analysis of a Class of Delayed Economic Model

Author

Listed:
  • Chuangxia Huang
  • Changlin Peng
  • Xiaohong Chen
  • Fenghua Wen

Abstract

This investigation aims at developing a methodology to establish stability and bifurcation dynamics generated by a class of delayed economic model, whose state variable is described by the scalar delay differential equation of the form d2p(t)/dt2 = −μδ(p(t))(dp(t)/dt) − μbp(t − τ1) −μ(a0p(t − τ2)/(a1 + p(t − τ2))) + μ(d0 − g0). At appropriate parameter values, linear stability and Hopf bifurcation including its direction and stability of the economic model are obtained. The main tools to obtain our results are the normal form method and the center manifold theory introduced by Hassard. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Our results extend and complement some earlier publications.

Suggested Citation

  • Chuangxia Huang & Changlin Peng & Xiaohong Chen & Fenghua Wen, 2013. "Dynamics Analysis of a Class of Delayed Economic Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:962738
    DOI: 10.1155/2013/962738
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    References listed on IDEAS

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    1. Manfredi, Piero & Fanti, Luciano, 2004. "Cycles in dynamic economic modelling," Economic Modelling, Elsevier, vol. 21(3), pages 573-594, May.
    2. Matsumoto, Akio & Szidarovszky, Ferenc, 2011. "Delay differential neoclassical growth model," Journal of Economic Behavior & Organization, Elsevier, vol. 78(3), pages 272-289, May.
    3. Howroyd, T. D. & Russell, A. M., 1984. "Cournot oligopoly models with time delays," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 97-103, October.
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    Cited by:

    1. Zigen Ouyang & Hongliang Liu, 2014. "Solvability for a Fractional Order Three‐Point Boundary Value System at Resonance," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Jian Liu & Lizhao Yan, 2014. "Multiple Solutions of Second‐Order Damped Impulsive Differential Equations with Mixed Boundary Conditions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
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    4. Zhifeng Dai, 2014. "Extension of Modified Polak‐Ribière‐Polyak Conjugate Gradient Method to Linear Equality Constraints Minimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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