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The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model

Author

Listed:
  • Carlo Bianca
  • Massimiliano Ferrara
  • Luca Guerrini

Abstract

A further generalization of an economic growth model is the main topic of this paper. The paper specifically analyzes the effects on the asymptotic dynamics of the Solow model when two time delays are inserted: the time employed in order that the capital is used for production and the necessary time so that the capital is depreciated. The existence of a unique nontrivial positive steady state of the generalized model is proved and sufficient conditions for the asymptotic stability are established. Moreover, the existence of a Hopf bifurcation is proved and, by using the normal form theory and center manifold argument, the explicit formulas which determine the stability, direction, and period of bifurcating periodic solutions are obtained. Finally, numerical simulations are performed for supporting the analytical results.

Suggested Citation

  • Carlo Bianca & Massimiliano Ferrara & Luca Guerrini, 2013. "The Time Delays’ Effects on the Qualitative Behavior of an Economic Growth Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:901014
    DOI: 10.1155/2013/901014
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    References listed on IDEAS

    as
    1. Invernizzi, Sergio & Medio, Alfredo, 1991. "On lags and chaos in economic dynamic models," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 521-550.
    2. Robert M. Solow, 1956. "A Contribution to the Theory of Economic Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 70(1), pages 65-94.
    3. Bao Shi & Fangwei Zhang & Shihe Xu, 2011. "Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-10, March.
    4. Bao Shi & Fangwei Zhang & Shihe Xu, 2011. "Hopf Bifurcation of a Mathematical Model for Growth of Tumors with an Action of Inhibitor and Two Time Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
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    Cited by:

    1. Beibei Wang & Min Zhao & Chuanjun Dai & Hengguo Yu & Nan Wang & Pengfei Wang, 2016. "Dynamics Analysis of a Nutrient‐Plankton Model with a Time Delay," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    2. José M. Gaspar, 2018. "Erratum to “Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand‐Aggregate Supply Model with Matlab”," Journal of Applied Mathematics, John Wiley & Sons, vol. 2018(1).
    3. Tianshi Lv & Qintao Gan & Qikai Zhu, 2016. "Stability and Bifurcation Analysis for a Class of Generalized Reaction‐Diffusion Neural Networks with Time Delay," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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