Delayed Feedback Control Of A Class Of Economic Chaos System

Chaos theory is currently one of the important topics in scientific research. As the financial crisis coming, people found many of the finance models were concerned with chaotic system. Chaos theory is known as "one of three" revolution in the 20th century science. People put forward a lot of method of control chaotic in order to take advantage of the chaos system. Delayed feedback control is one of the effective methods in control of chaos.This paper mainly discusses a class of chaotic nonlinear finance system with chaos characteristic. Because the system is chaos in some specific parameters, so this paper takes the delay feedback control method into the finance system, analysis the dynamic behavior of finance system with time delay, considers the control problem about chaos phenomenon.For the system adding delay feedback, this paper first calculates the fixed point. Then we take the fixed point to the origin to get a new system, and get the new characteristic equation, analysis the situation about the characteristic equations root, discuss when the system with time delays will experience Hopf branch. Because the fixed point has switch phenomenon, so this paper lists the stability and unstable interval of the fixed point. Then this paper use the center manifold theory and the standard type method to calculate some important parameters which decide the characteristic of Hopf branch, and then discuss the direction of Hopf branch and the stability of periodic solution. Finally, this paper uses computing functions and drawing function of Matlab, tests the theory analysis results before through numerical simulation. We simulate the stable periodic solution and fixed point, confirm that the theory analysis is correct from the visual angle.