Dynamics Analysis of a Class of Delayed Economic Model

This investigation aims at developing a methodology to establish stability and bifurcation dynamics generated by a class of delayed economic model, whose state variable is described by the scalar delay differential equation of the form d2p(t)/dt2=−μδ(p(t))(dp(t)/dt)−μbp(t−τ1) −μ(a0p(t−τ2)/(a1+p(t−τ2)))+μ(d0−g0). At appropriate parameter values, linear stability and Hopf bifurcation including its direction and stability of the economic model are obtained. The main tools to obtain our results are the normal form method and the center manifold theory introduced by Hassard. Simulations show that the theoretically predicted values are in excellent agreement with the numerically observed behavior. Our results extend and complement some earlier publications.