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Center Manifold Reduction and Perturbation Method in a Delayed Model with a Mound‐Shaped Cobb‐Douglas Production Function

Author

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  • Massimiliano Ferrara
  • Luca Guerrini
  • Giovanni Molica Bisci

Abstract

Matsumoto and Szidarovszky (2011) examined a delayed continuous‐time growth model with a special mound‐shaped production function and showed a Hopf bifurcation that occurs when time delay passes through a critical value. In this paper, by applying the center manifold theorem and the normal form theory, we obtain formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. Moreover, Lindstedt’s perturbation method is used to calculate the bifurcated periodic solution, the direction of the bifurcation, and the stability of the periodic motion resulting from the bifurcation.

Suggested Citation

  • Massimiliano Ferrara & Luca Guerrini & Giovanni Molica Bisci, 2013. "Center Manifold Reduction and Perturbation Method in a Delayed Model with a Mound‐Shaped Cobb‐Douglas Production Function," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:738460
    DOI: 10.1155/2013/738460
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    References listed on IDEAS

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    1. Luca Guerrini & Mauro Sodini, 2013. "Nonlinear Dynamics in the Solow Model with Bounded Population Growth and Time‐to‐Build Technology," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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    4. Akio Matsumoto & Ferenc Szidarovszky, 2013. "Asymptotic Behavior of a Delay Differential Neoclassical Growth Model," Sustainability, MDPI, vol. 5(2), pages 1-16, January.
    5. Luca Guerrini & Mauro Sodini, 2013. "Nonlinear Dynamics in the Solow Model with Bounded Population Growth and Time-to-Build Technology," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-6, November.
    6. BOUCEKKINE, Raouf & FABBRI, Giorgio & PINTUS, Patrick, 2012. "On the optimal control of a linear neutral differential equation arising in economics," LIDAM Reprints CORE 2449, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Juan Liu & Carlo Bianca & Luca Guerrini, 2016. "Dynamical Analysis of a Computer Virus Model with Delays," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).

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