Chaotic dynamic behavior analysis and control for a financial risk system

According to the risk management process of financial market, a financial risk dynamic system is constructed in this paper. Through analyzing the basic dynamic property, we obtain the conditions for stability and bifurcation of the system based on Hopf bifurcation theory of nonlinear dynamical systems. In order to make the system's chaos disappear, we select the feedback gain matrix to design a class of chaotic controller. Numerical simulations are performed to reveal the change process of financial market risk. It is shown that, when the parameter of risk transmission rate changes, the system gradually comes into chaos from the asymptotically stable state through bifurcation. Besides, the controller can control chaos effectively.