一类分数阶混沌金融系统的复杂性演化研究

辛宝贵; 陈通; 刘艳芹

doi:10.7498/aps.60.048901

摘要

物理学理论与方法在经济与金融领域中的成功应用催生了一个新的科学分支——经济物理学(econophysics).分数阶微积分系统的复杂动力学现象受到了越来越多学者的关注.本文定性地分析一类分数阶混沌金融系统的均衡解的稳定性及Hopf分岔发生的条件,并运用亚当斯-巴什福斯-莫尔顿预估-校正的有限差分法,通过分岔图、相图和时间序列图对该系统的复杂性演化行为进行仿真研究.

关键词:

A novel science branch, econophysics, is set up because various physical theories and methods are applied to economic and financial fields. More and more researchers are fascinated by the complex dynamical behavior of the fractional-order dynamical system. The paper analyzes the stability of the fractional-order financial system, and then simulates the generalized model complexity with Adams-Bashforth-Moulton predictor-corrector scheme by using bifurcation diagram, phase portrait and history time-series.

Keywords:

作者及机构信息

1.
天津大学管理与经济学部,天津 300072

基金项目: 中国博士后科学基金(批准号:20100470783),高等学校博士学科点专项科研基金(批准号:20090032110031) 和国家自然科学基金(批准号:60904063)资助的课题.

Authors and contacts

1.
School of Management, Tianjin University, Tianjin 300072, China

参考文献

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[2]	Challet D, Zhang Y 1997 Phys. A 246 407
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[4]	Guo R, Huang H 2008 Chin. Phys. B 17 1698
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[6]	Gou C, Gao F, Chen F 2010 Chin. Phys. B 19 110514
[7]	Wang Z, Xu Z, Huang J, Zhang L 2010 Chin. Phys. B 19 100204
[8]	Zhou P,Wei L, Cheng X 2009 Chin. Phys. B 18 2674
[9]	Zhang R, Yang S 2009 Chin. Phys. B 18 3295
[10]	Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇、谢勇 2010 物理学报 59 2147]
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[12]	Liu D, Yan X M 2010 Acta Phys. Sin. 59 3747 (in Chinese) [刘丁、闫晓妹 2010 物理学报 59 3747]
[13]	Huang L L 2011 Acta Phys. Sin. 60 010505 (in Chinese) [黄丽莲 2011 物理学报 60 010505]
[14]	Jiang X, Xu M, Qi H 2010 Nonlinear Anal-Real 11 262
[15]	Liu Y, Ma J 2009 Commun. Theor. Phys. 52 857
[16]	Chen W 2008 Chaos, Soliton. Fract. 36 1305
[17]	Song L, Xu S, Yang J 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 616
[18]	Ahmad W, El-Khazali R 2007 Chaos, Soliton. Fract. 33 1367
[19]	Puu T 1997 Nonlinear economic dynamics (NY:Springer Verlag)
[20]	Xin BG, Ma J, Gao Q 2009 Chaos, Soliton. Fract. 42 2425
[21]	Sprott J 2003 Chaos and time-series analysis (NY:Oxford Univ. Press)
[22]	Huang D, Li H Q 1993 Theory and method of the nonlinear economics (Chengdu:Sichuan Univ. Press) (in Chinese) [黄登仕、李后强 1993 非线性经济学的理论和方法(成都:四川大学出版社)]
[23]	Qiu T 2010 IMF head:No asset bubble in Asia. In Wen Wei Po (HK:Wen Wei Po Press)
[24]	Jiang X, Xu M 2010 Phys. A 389 3368
[25]	Podlubny I 1999 Fractional differential equations (NY:Academic press).
[26]	Diethelm K, Ford N, Freed A 2002 Nonlinear Dynam. 29 3
[27]	Deng W, Li C 2008 Phys. Lett. A 372 401
[28]	Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402(in Chinese) [胡建兵、韩焱、赵灵冬 2010 物理学报 58 4402]
[29]	Deng W 2010 Nonlinear Anal-Theor. 72 1768

施引文献

[1]	Arthur W 1994 Am. Econ. Rev. 84 406
[2]	Challet D, Zhang Y 1997 Phys. A 246 407
[3]	Huang Z,Chen Y,Zhang Y, Wang Y 2007 Chin. Phys. 16 975
[4]	Guo R, Huang H 2008 Chin. Phys. B 17 1698
[5]	Chen W D, Xu H, Guo Q 2010 Acta Phys. Sin. 59 4514 (in Chinese) [陈卫东、徐华、郭琦 2010 物理学报 59 4514]
[6]	Gou C, Gao F, Chen F 2010 Chin. Phys. B 19 110514
[7]	Wang Z, Xu Z, Huang J, Zhang L 2010 Chin. Phys. B 19 100204
[8]	Zhou P,Wei L, Cheng X 2009 Chin. Phys. B 18 2674
[9]	Zhang R, Yang S 2009 Chin. Phys. B 18 3295
[10]	Liu Y, Xie Y 2010 Acta Phys. Sin. 59 2147 (in Chinese) [刘勇、谢勇 2010 物理学报 59 2147]
[11]	Wang M, Wang X 2010 Acta Phys. Sin. 59 1583 (in Chinese) [王明军、王兴元 2010 物理学报 59 1583]
[12]	Liu D, Yan X M 2010 Acta Phys. Sin. 59 3747 (in Chinese) [刘丁、闫晓妹 2010 物理学报 59 3747]
[13]	Huang L L 2011 Acta Phys. Sin. 60 010505 (in Chinese) [黄丽莲 2011 物理学报 60 010505]
[14]	Jiang X, Xu M, Qi H 2010 Nonlinear Anal-Real 11 262
[15]	Liu Y, Ma J 2009 Commun. Theor. Phys. 52 857
[16]	Chen W 2008 Chaos, Soliton. Fract. 36 1305
[17]	Song L, Xu S, Yang J 2010 Commun. Nonlinear Sci. Numer. Simulat. 15 616
[18]	Ahmad W, El-Khazali R 2007 Chaos, Soliton. Fract. 33 1367
[19]	Puu T 1997 Nonlinear economic dynamics (NY:Springer Verlag)
[20]	Xin BG, Ma J, Gao Q 2009 Chaos, Soliton. Fract. 42 2425
[21]	Sprott J 2003 Chaos and time-series analysis (NY:Oxford Univ. Press)
[22]	Huang D, Li H Q 1993 Theory and method of the nonlinear economics (Chengdu:Sichuan Univ. Press) (in Chinese) [黄登仕、李后强 1993 非线性经济学的理论和方法(成都:四川大学出版社)]
[23]	Qiu T 2010 IMF head:No asset bubble in Asia. In Wen Wei Po (HK:Wen Wei Po Press)
[24]	Jiang X, Xu M 2010 Phys. A 389 3368
[25]	Podlubny I 1999 Fractional differential equations (NY:Academic press).
[26]	Diethelm K, Ford N, Freed A 2002 Nonlinear Dynam. 29 3
[27]	Deng W, Li C 2008 Phys. Lett. A 372 401
[28]	Hu J B, Han Y, Zhao L D 2009 Acta Phys. Sin. 58 4402(in Chinese) [胡建兵、韩焱、赵灵冬 2010 物理学报 58 4402]
[29]	Deng W 2010 Nonlinear Anal-Theor. 72 1768

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