Research On The Application Of Time - Delay Dynamic System In Economic Model

The bifurcation theory of ordinary differential equations is widely used in many disciplines, and the branch of the delay differential equation is an important issue.In this paper, we mainly study the dynamic system of differential equations of two economic classes. One of them is a kind of advertising -the shopping level model with time delay,, the other is the investment model with time delay.The first chapter, we mainly about the background and research status of this issue.In the second chapter, some basic definitions and theorem are introduced to the issue.In this chapter,a advertisement-shopping model with time delay is investigat-ed. We first consider the stability of the positive equilibrium and the existence of local Hopf bifurcations.By using the normal form theory and center manifold theorem,we analyze the stability, direction and periodic solution of the proposed system. Finally, the numerical simulations are given to illustrate the theoretical analysis.The fourth chapter is investigate the stability of Hopf bifurcation and period solutions of the investment model with time delay. In this chapter, we mainly add the time delay in the price equation, and obtain the eigenvalues of the characteristic equation with time delay,.By using the normal form theory and center manifold theorem to derive the direction and periodic solution of Hopf bifurcation.Finally, the conclusion can be convinced.