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

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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, Hindawi, vol. 2013, pages 1-6, December.
    • Handle: RePEc:hin:jnlaaa:738460
    DOI: 10.1155/2013/738460
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    Cited by:

    1. Jana, Debaldev & Pathak, Rachana & Agarwal, Manju, 2016. "On the stability and Hopf bifurcation of a prey-generalist predator system with independent age-selective harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 252-273.

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