57. Stability and Hopf Bifurcation of a Four-Dimensional Dynamic Economic System

In this paper, first of all, a four-dimensional dynamic economic system is established. First, choosing the saving rate as the bifurcation parameter, the stability and Hopf bifurcation of the system are studied. Then, a example of simulation of the model is used to prove the derived results in Sect57.2. Furthermore, a time-delayed feedback is added to the dynamic finance system. Choosing the delay as the bifurcation parameter, the local stability and the existence of Hopf bifurcation of the model with delay are researched. Stability changes and Hopf bifurcation happens while the delay passes through a critical value. We can see that increasing the delay can lead the dynamic economic system to fluctuate. Then, a numerical example is taken to confirm the theoretical results obtained in Sect.57.3. Finally, some conclusions are made. This paper has an important theoretical and practical significance.