Stability Analysis Of Enterprise Competitive Models With Time Delay

The stability of financial system has been focused on by a number of economists and mathematicians. The existences of delay have caused great difficulties in system control. Normally, the delay will lead to the loss of system stability. Therefore, the discussion on the stability of financial market is necessary to management and understanding of financial system.This paper is divided into two parts:In the second chapter of this article, a three-dimensional enterprise competitive model with time delay is considered. Under the Hopf bifurcation theory and stability theory, we analyze the impact of time delay to characteristic of equilibrium. Moreover, we give the formula for determining the direction of the stability of bifurcating periodic solutions and the Hopf bifurcation. Finally, numerical simulations are performed to support the analytical results.In the third chapter of this article considers a three-dimensional macro economic model with time delay. Under the Hopf bifurcation theory and stability theory, We derive the equation describing the flow on the center manifold and analyze the impact of time delay to characteristic of equilibrium. Then the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form method and center manifold theorem.