Chaotic dynamic behavior analysis and control for a financial risk system

doi:10.1088/1674-1056/22/3/030509

中国物理B ›› 2013, Vol. 22 ›› Issue (3): 30509-030509.doi: 10.1088/1674-1056/22/3/030509

Chaotic dynamic behavior analysis and control for a financial risk system

张晓丹^a, 刘祥东^b, 郑媛^a, 刘澄^b

a School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
b Dongling School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China

收稿日期:2012-01-28 修回日期:2012-11-20 出版日期:2013-02-01 发布日期:2013-02-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 70271068).

Chaotic dynamic behavior analysis and control for a financial risk system

Zhang Xiao-Dan (张晓丹)^a, Liu Xiang-Dong (刘祥东)^b, Zheng Yuan (郑媛)^a, Liu Cheng (刘澄)^b

a School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China;
b Dongling School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China

Received:2012-01-28 Revised:2012-11-20 Online:2013-02-01 Published:2013-02-01
Contact: Zhang Xiao-Dan E-mail:bkdzxd@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 70271068).

摘要/Abstract

摘要： 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.

关键词: chaos attractor, Hopf bifurcation, financial risk, chaos feedback control

Abstract: 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.

Key words: chaos attractor, Hopf bifurcation, financial risk, chaos feedback control

中图分类号: (High-dimensional chaos)

05.45.Jn

05.45.Gg (Control of chaos, applications of chaos) 05.45.Pq (Numerical simulations of chaotic systems) 89.65.Gh (Economics; econophysics, financial markets, business and management)

张晓丹, 刘祥东, 郑媛, 刘澄. Chaotic dynamic behavior analysis and control for a financial risk system[J]. 中国物理B, 2013, 22(3): 30509-030509.

Zhang Xiao-Dan (张晓丹), Liu Xiang-Dong (刘祥东), Zheng Yuan (郑媛), Liu Cheng (刘澄). Chaotic dynamic behavior analysis and control for a financial risk system[J]. Chin. Phys. B, 2013, 22(3): 30509-030509.

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Chaotic dynamic behavior analysis and control for a financial risk system

Chaotic dynamic behavior analysis and control for a financial risk system

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