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

Abstract

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 “high” 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–Poincaré 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.