Dynamic Analysis of a New Financial System with Diffusion Effect and Two Delays

Abstract

The dynamic behavior of a new financial system with diffusion effect and two delays is studied. The local stability of equilibrium is studied by analyzing the corresponding characteristic equation and developing the crossing curve method. Hopf bifurcation curves are obtained by three procedures and the critical value of delay of Hopf bifurcation is obtained. By using the central manifold theorem and the normal form theory of partial differential equations, the normal form of Hopf bifurcation with two delays is derived, and the bifurcation direction and the stability of periodic solution are determined. The numerical simulations not only verify these theoretical results, but also show that double Hopf bifurcation may occur and the two delays play a key role in chaos suppression. This study has important theoretical value of innovation and practical value in the macro-economic system.