具有分数阶非线性金融风险系统模型的动力学行为控制  

Dynamic analysis and control of financial risk system model with fractional order nonlinearity

作　　者：李博 刘国欣[3] 张霞 LI Bo;LIU Guoxin;ZHANG Xia(School of Economics and Management,Hebei University of Technology,Tianjin 300000,China;Hebei Branch,Bank of China Limited,Shijiazhuang 050000,China;School of Mathematics and Physics,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Traffic and Transportation,Shijiazhuang Tiedao University,Shijiazhuang 050043,China)

机构地区：[1]河北工业大学经济管理学院,天津300000 [2]中国银行股份有限公司河北省分行,河北石家庄050000 [3]石家庄铁道大学数理学院,河北石家庄050043 [4]石家庄铁道大学交通运输学院,河北石家庄050043

出　　处：《安徽大学学报（自然科学版）》2022年第6期27-34,共8页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11471218);河北省高等学校科学技术研究基金资助项目(ZD20131017)。

摘　　要：基于非线性动力学理论讨论了具有记忆特性的分数阶金融系统风险模型,研究系统在平衡点处的稳定性,分析表明该分数阶系统模型描述的金融风险系统存在分岔、混沌等极其复杂的动力学行为.通过逆优化和增加反馈增益两种控制方法对系统混沌动力学行为进行干预控制,并讨论了两种控制方法的鲁棒性,发现增加反馈增益控制及加大其反馈增益系数,可提高系统的稳定运动控制效果.研究结果为金融系统规避风险提供理论依据.Based on the theory of nonlinear dynamics, this paper constructed a fractional order financial system risk model with memory characteristics. The stability of the system at the equilibrium point was studied. The analysis showed that the financial risk system described by the fractional order system model had very complex dynamical behaviors such as bifurcation and chaos. Furthermore, the chaotic behavior in the system was controlled by two methods: inverse optimization control and increasing feedback gain control. The robustness of the two control methods was discussed. It was found that increasing feedback gain control and increasing its feedback gain coefficient could improve the control effect of the system. The results can provide theoretical basis for the economic system to avoid financial risks.

关 键 词：金融风险系统 非线性动力学 分数阶理论 混沌运动及控制 

分 类 号：O415.5[理学—理论物理]