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

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. [ABSTRACT FROM AUTHOR]