Abstract: We investigate the effect of delayed feedbacks on a finance system. Choosing the delays as the bifurcation parameters, the local stability of the equilibrium is studied and the Hopf bifurcation and Hopf-zero bifurcation happen while the delay passes through a sequence of critical values. For determining the properties of bifurcating periodic solutions, we derive explicit formulae by using the normal form method and the center manifold theory. By designing appropriate feedback strength and delay, chaotic oscillation can be controlled to be a stable equilibrium or stable periodic orbits. Finally, a numerical example is taken to confirm the theoretical results.

Key words: Stability, Hopf bifurcation, Hopf-zero bifurcation, Chaos control