Dynamics Analysis in an Economic Growth Model with Logistic Population and Delay

摘要

In this paper, we will analyze the mathematical model associated to an economic growth process with logistic population growth and delay. Mathematical modeling of this economical growth process leads to an optimal control problem with delay. We study the Hopf bifurcation of this growth model in which production occurs with delay while new capital is installed (time-to-build). The time-to-build technology is shown to yield a system of differential functional equations with a steady state. This steady state exhibits the Hopf bifurcation and we determine the direction and stability of the bifurcating periodic solutions by applying the normal form theory and the center manifold theorem.