分数阶混沌金融模型的时滞反馈控制策略

徐昌进; 段振华

doi:10.21656/1000-0887.400323

分数阶混沌金融模型的时滞反馈控制策略

doi: 10.21656/1000-0887.400323

徐昌进¹,
段振华²

¹贵州财经大学贵州省经济系统仿真重点实验室, 贵阳 550025;²广州铁路职业技术学院基础课部, 广州 510430

基金项目: 国家自然科学基金(61673008)；贵州省高层次创新型人才培养计划:百层次人才项目(［2016］5651)；

详细信息

作者简介:
徐昌进(1970—)，男，教授，博士(E-mail: xcj403@126.com);段振华(1964—)，男，副教授(通讯作者. E-mail: gtxyjwc@163.com).

中图分类号: O175.13
计量
- 文章访问数: 1675
- HTML全文浏览量: 455
- PDF下载量: 249
- 被引次数: 0
出版历程
- 收稿日期: 2019-10-25
- 修回日期: 2020-02-12
- 刊出日期: 2020-12-01

A Delayed Feedback Control Method for Fractional-Order Chaotic Financial Models

XU Changjin>¹,
DUAN Zhenhua²

¹Guizhou Key Laboratory of Economics System Simulation, Guizhou University of Finance and Economics, Guiyang 550025, P.R.China;²Department of Basic Sciences, Guangzhou Railway Polytechnic,Guangzhou 510430, P.R.China

Funds: The National Natural Science Foundation of China(61673008)

摘要

摘要: 该文研究了一类分数阶金融模型的混沌控制问题.运用时滞反馈控制法成功控制了金融模型的混沌行为,建立了该模型平衡点稳定及Hopf分支存在的充分条件,揭示了时滞和分数阶的阶数对该模型的稳定性和分支的影响.计算机模拟验证了理论分析的正确性,研究结果为维持金融稳定提供了理论依据.
- 金融模型 /
- 分数阶 /
- Hopf分支 /
- 稳定性 /
- 混沌控制 /
- 时滞反馈控制法
Abstract: The chaos control of a class of fractional-order delayed financial models was studied. The chaotic behavior was successfully controlled by means of the time delayed feedback control method. The sufficient condition to ensure the stability and the existence of the Hopf bifurcation was established. The effects of the delay and the fractional order on the stability and bifurcation were revealed. Numerical simulations verify the correctness of the theoretical analysis. The obtained results provide a theoretical foundation for financial stability.
- financial model /
- fractional order /
- Hopf bifurcation /
- stability /
- chaos control /
- delayed feedback control method

HTML全文

参考文献(18)

[1]	GAO Q, MA J H. Chaos and Hopf bifurcation of a finance system[J]. Nonlinear Dynamics,2009,58(1/2): 209-216.
[2]	ZHANG J G, NAN J, CHU Y D, et al. Stochastic Hopf bifurcation of a novel finance chaotic system[J]. Journal of Nonlinear Science and Applications,2016,9(5): 2727-2739.
[3]	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[J]. 应用数学和力学, 2001,22(11): 1119-1128.(MA Junhai, CHEN Yushu. Study for bifurcation topological structure and the global complicated character of a kind of non-linear finance system [J]. Applied Mathematics and Mechanics,2001,22(11): 1119-1128.(in Chinese))
[4]	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[J]. 应用数学和力学, 2001,22(12): 1236-1242.(MA Junhai, CHEN Yushu. Study for bifurcation topological structure and the global complicated character of a kind of non-linear finance system [J]. Applied Mathematics and Mechanics,2001,22(12): 1236-1242.(in Chinese))
[5]	ZHANG L L, CAI G L, FANG X L. Stability for a novel time-delay financial hyperchaotic system by adaptive periodically intermittent linear control[J]. Journal of Applied Analysis and Computation,2017, 7(1): 79-91.
[6]	林勇新, 陈予恕, 曹庆杰. 一类金融系统行为的非线性混沌分析[J]. 应用数学和力学, 2010,31(10): 1239-1248.(LIN Yongxin, CHEN Yushu, CAO Qingjie. Nonlinear and chaotic analysis of a financial complex system[J]. Applied Mathematics and Mechanics,2010,31(10): 1239-1248.(in Chinese))
[7]	CAI G L, YAO L, HU P, et al. Adaptive full state hybrid function projective synchronization of financial hyperchaotic systems with uncertain parameters[J]. Discrete and Continuous Dynamical Systems(Series B),2013,18(8): 2019-2028.
[8]	MA J H, BANGURA H I. Complexity analysis research of financial and economic system under the condition of three parameters’ change circumstances[J]. Nonlinear Dynamics,2012,70(4): 2313-2326.
[9]	ABD-ELOUAHAB M S, HAMRI N E, WANG J W. Chaos control of a fractional-order financial system[J]. Mathematical Problems in Engineering,2010,2010: 270646. DOI: 10.1155/2010/270646.
[10]	HAJIPOUR A, TAVAKOLI H. Analysis and circuit simulation of a novel nonlinear fractional incommensurate order financial system[J]. Optik,2016,127(22): 10643-10652.
[11]	HUANG C D, CAI L M, CAO J D. Linear control for synchronization of fractional-order time-delayed chaotic financial system[J]. Chaos, Solitons & Fractals,2018,113: 326-332.
[12]	CHEN W C. Dynamics and control of a financial system with time-delayed feedbacks[J]. Chaos, Solitons & Fractals,2008,37: 1198-1207.
[13]	ZHANG X B, ZHUA H L. Hopf bifurcation and chaos of a delayed finance system[J]. Complexity,2019,2019: 6715036. DOI: 10.1155/2019/6715036.
[14]	ZHANG R Y. Bifurcation analysis for a kind of nonlinear finance system with delayed feedback and its application to control of chaos[J]. Journal of Applied Mathematics,2012,2012: 316390. DOI: 10.1155/2012/316390.
[15]	CHEN X L, LIU H H, XU C L. The new result on delayed finance system[J]. Nonlinear Dynamics,2014,78(3): 1989-1998.
[16]	MIRCEA G, NEAMTU M, BUNDAU O, et al. Uncertain and stochastic financial models with multiple delays[J]. International Journal of Bifurcation and Chaos,2012,22(6): 19.
[17]	杜伟霞, 张思进, 殷珊. 一类对称碰撞系统的间歇混沌控制方法[J]. 应用数学和力学, 2018,39(10): 1149-1158.(DU Weixia, ZHANG Sijin, YIN Shan. An intermittent chaos control method for a class of symmetric impact systems[J]. Applied Mathematics and Mechanics,2018,39(10): 1149-1158.(in Chinese))
[18]	张艳龙, 王丽, 石建飞. Duffing系统在双参数平面上的分岔演化过程[J]. 应用数学和力学, 2018,39(3): 324-333.(ZHANG Yanlong, WANG Li, SHI Jianfei. Bifurcation evolution of Duffing systems on 2-parameter planes[J]. Applied Mathematics and Mechanics,2018,39(3): 324-333.(in Chinese))