Nonlinear dynamics in a Solow model with delay and non-convex technology

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• 作者：Massimiliano Ferrara ; Luca Guerrini ; Mauro Sodini
• 关键词：Solow growth model ; Time delay ; Hopf bifurcation ; Lindstedt perturbation
• 刊名：Applied Mathematics and Computation
• 出版年：1 February, 2014
• 年：2014
• 卷：228
• 期：Complete
• 页码：1-12
• 全文大小：1052 K

文摘

In this paper we propose an extension to the classic Solow model by introducing a non-concave production function and a time-to-build assumption. The capital accumulation equation is given by a delay differential equation that has two non-trivial stationary equilibria. By choosing time delay as the bifurcation parameter, we demonstrate that the 鈥渉igh鈥?stationary solution may lose its stability and a Hopf bifurcation occurs when the delay passes through critical values. 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. In addition, the Lindstedt-Poincar茅 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. The Hopf bifurcation is found to be supercritical. Finally, numerical simulations are given to justify the validity of the theoretical analysis.