Chaotic dynamic behavior analysis and control for a financial risk system

According to the risk management process of financial markets, a financial risk dynamic system is constructed in this paper. Through analyzing the basic dynamic properties, we obtain the conditions for stability and bifurcation of the system based on Hopf bifurcation theory of nonlinear dynamic 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. The controller can then control the chaos effectively.

[1]  陈增强,et al.  The generation of a hyperchaotic system based on a three-dimensional autonomous chaotic system , 2006 .

[2]  Empirical tests of chaotic dynamics in market volatility , 1995 .

[3]  R. Day.  Irregular Growth Cycles , 2016 .

[4]  李宁,et al.  Bifurcations and chaos control in discrete small-world networks , 2012 .

[5]  Lequan Min,et al.  A Generalized Synchronization Theorem for an Array of Differential Equations with Application to Secure Communication , 2005, Int. J. Bifurc. Chaos.

[6]  Ping Chen,et al.  Deterministic chaos and fractal attractors as tools for nonparametric dynamical econometric inference: with an application to the divisia monetary aggregates , 1988 .

[7]  Zhang Xiaodan,et al.  Estimating the bound for the generalized Lorenz system , 2010 .

[8]  Ping Chen,et al.  Empirical and theoretical evidence of economic chaos , 1988 .

[9]  曹晖,et al.  A new four-dimensional hyperchaotic Lorenz system and its adaptive control , 2011 .

[10]  Chi-Chuan Hwang,et al.  A nonlinear feedback control of the Lorenz equation , 1999 .

[11]  Zhang Wei,et al.  Projective synchronization of a hyperchaotic system via periodically intermittent control , 2012 .

[12]  Rong Hu,et al.  Chaotic dynamics and chaos control in differentiated Bertrand model with heterogeneous players , 2012, Grey Syst. Theory Appl..

[13]  H. N. Agiza,et al.  Controlling chaos for the dynamical system of coupled dynamos , 2002 .

[14]  A. A. Elsadany,et al.  Chaotic dynamics in nonlinear duopoly game with heterogeneous players , 2004, Appl. Math. Comput..

[15]  David Hsieh.  Chaos and Nonlinear Dynamics: Application to Financial Markets , 1991 .

[16]  M. M. El-Dessoky,et al.  Controlling chaotic behaviour for spin generator and Rossler dynamical systems with feedback control , 2001 .

[17]  Brice V. Dupoyet,et al.  Replicating Financial Market Dynamics with a Simple Self-Organized Critical Lattice Model , 2010, 1010.4831.

[18]  Gustav Feichtinger,et al.  Chaos in nonlinear dynamical systems exemplified by an R & D model , 1993 .

[19]  William A. Barnett,et al.  Empirical chaotic dynamics in economics , 1992, Ann. Oper. Res..

[20]  Wei-Ching Chen,et al.  Nonlinear dynamics and chaos in a fractional-order financial system , 2008 .

[21]  Michael J. Stutzer,et al.  Chaotic dynamics and bifurcation in a macro model , 1980 .

[22]  B. LeBaron,et al.  Nonlinear Dynamics and Stock Returns , 2021, Cycles and Chaos in Economic Equilibrium.

[23]  C. Hommes.  Periodic, almost periodic and chaotic behaviour in Hicks' non-linear trade cycle model , 1993 .