期刊信息
- 刊名： 河北师范大学学报（自然科学版）Journal of Hebei Normal University (Natural Science)
- 主办： 河北师范大学
- ISSN： 1000-5854
- CN： 13-1061/N
- 中国科技核心期刊
- 中国期刊方阵入选期刊
- 中国高校优秀科技期刊
- 华北优秀期刊
- 河北省优秀科技期刊
Complexity Simulation of a Class of Fractional-order Nonlinear Financial System
摘要/Abstract
利用混沌与分岔理论研究了一类分数阶金融系统的混沌动力学行为.首先,分析了该系统的稳定性、平衡点.其次,借助预估校正法,得到了关于微分阶数储蓄量、投资成本和商品需求弹性的分岔图、相图和时间历程图,由分岔图和相图可知该系统会出现非常复杂的动力学行为,利用混沌与分岔理论进一步研究了不同参数配比的相关问题,分别模拟了各金融指标对分数阶金融系统复杂性演化行为的影响,得出了一些有意义的结果,可以为经济金融管理部门对金融系统调控提供理论依据.
The chaos dynamic behaviors of a class of fractional order financial systems based on chaos and bifurcation theory were discussed in this paper. Firstly, the stability of the system and the equilibrium point are analyzed. Secondly, the bifurcation diagram and phase diagram of differential order, savings, investment cost and commodity demand elasticity are obtained by a predictive correction method. The bifurcation diagram and phase diagram show that the system will have very complex dynamic behaviors. Furthermore, how to use the chaos theory of mixed bifurcation under different parameterratios was studied, simulates the influence of various financial indicators on the complexity evolution behavior of fractional financial system was simulated, and obtains some meaningful research results was obtained. These results provides a theoretical basis for the financial managers to regulate the financial system.
关键词
参考文献 10
- [1] 成思危.复杂科学与管理[J].中国科学院院刊,1999(3):175-183.doi：10.16418/j.issn.1000-3045.1999.03.004 CHENG Siwei. Complex Science and Management[J]. Bulletin of the Chinese Academy of Sciences,1999(3):175-183.
- [2] 陈燕燕.一类金融混沌系统的线性控制模型[J].金融数学，2017，34(4):48-52.doi：10.16339/j.cnki.hdjjsx.2018.04.009 CHEN Yanyan. Linear Control Model for a Class of Financial Chaotic Systems[J]. Financial Mathematics,2017,34(4):48-52.
- [3] 王晶囡，吕静，李想.一类金融系统的分岔分析与混沌[J].动力学与控制学报，2016，14(6):508-512.doi：10.6052/1672-6553-2015-086 WANG Jingnan,LYU Jing,LI Xiang. Bifurcation Analysis and Chaos for a Class of Financial Systems [J]. Journal of Dynamics and Control,2016,14(6):508-512.
- [4] 黄登仕，李后强.非线性金融学的理论和方法[M].成都:四川大学出版社，1993. HUANG Dengshi,LI Houqiang. The Theory and Method of Nonlinear Finance[M]. Chengdu:Sichuan University Press,1993.
- [5] 李想，赵小山.一类金融系统的分数阶和整数阶混沌同步[J].高师理科学刊，2020，40(7):1-4.doi：10.3969/j.issn.1007-9831.2020.07.001 LI Xiang，ZHAO Xiaoshan. Fractional and Integer Order Chaotic Synchronization of a Financial System [J]. Journal of Advanced Science,2020,40(7):1-4.
- [6] 马军海，陈予恕．一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究(Ⅰ)[J].应用数学和力学，2001，22(11):1119-1128.doi：10.3321/j. issn.10000887.2001.11.002 MA Junhai,CHEN Yushu.Study for the Bifurcation Topological Structure and the Global Complicated Character of a Kind of Non-linear Finance System(Ⅰ)[J]. Applied Mathematics and Mechanics,2001,22(11):1119-1128.
- [7] 马军海，陈予恕.一类非线性金融系统分岔混沌拓扑结构与全局复杂性研究(Ⅱ)[J].应用数学和力学，2001，22(12):1236-1242.doi：10.3321/j.issn.1000-0887.2001.12.003 MA Junhai,CHEN Yushu. Study for the Bifurcation Topological Structure and the Global Complicated Character of a Kind of Non-linear Finance System(Ⅱ)[J]. Applied Mathematics and Mechanics,2001,22(12):1236-1242.
- [8] ZHANG Jiming， LI Xiaoshuang, YANG Qiu.A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems [J]. Discrete Dynamics in Nature and Society，2017(1):1-7. doi： 10.1155/2017/9129605ISBN. 1026-0226
- [9] DIETHELM K，FORD N J，FREED A D. A Predictor-corrector Approach for the Numerical Solution of Fractional Differential Equations [J]. Nonlinear Dynamics，2002，29(2/3/4):3-22. doi： 10.1023/A. 1016592219341ISBN. 0924-090X
- [10] DANCA M F，ROMERA M，PASTOR G，et al. Finding Attractors of Continuous-time Systems by Parameter Switching [J]. Nonlinear Dynamics，2012，67:2317-2342. doi： 10.1007/s11071-011-0172-6