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On the Dalgaard-Strulik Model with Logistic Population Growth Rate and Delayed-Carrying Capacity

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Abstract

Recently Dalgaard and Strulik have proposed (in Resour. Energy Econ. 33:782–797, 2011) an energy model of capital accumulation based on the mathematical framework developed by Solow-Swan and coupled with Cobb-Douglas production function (Solow in Q. J. Economics 70:65–94, 1956; Swan in Econ. Rec. 32(63):334–361, 1956). The model is based on a constant rate of population growth assumption. The present paper, according to the analysis performed by Yukalov et al. (Physica D 238:1752–1767, 2009), improves the Dalgaard-Strulik model by introducing a logistic-type equation with delayed carrying capacity which alters the asymptotic stability of the relative steady state. Specifically, by choosing the time delay as a bifurcation parameter, it turns out that the steady state loses stability and a Hopf bifurcation occurs when time delay passes through critical values. The results are of great interest in the applied and theoretical economics.

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Authors and Affiliations

  1. Dipartimento di Scienze Matematiche, Politecnico, 10129, Torino, Italy

    Carlo Bianca

  2. Dipartimento di Matematica per le Scienze Economiche e Sociali, Università di Bologna, 40126, Bologna, Italy

    Luca Guerrini

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  1. Carlo Bianca
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  2. Luca Guerrini
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Correspondence to Carlo Bianca.

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Bianca, C., Guerrini, L. On the Dalgaard-Strulik Model with Logistic Population Growth Rate and Delayed-Carrying Capacity. Acta Appl Math 128, 39–48 (2013). https://doi.org/10.1007/s10440-013-9800-0

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  • DOI: https://doi.org/10.1007/s10440-013-9800-0

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