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Complexity evolvement of a chaotic fractional-orderfinancial system

Xin Bao-Gui Chen Tong Liu Yan-Qin

Complexity evolvement of a chaotic fractional-orderfinancial system

Xin Bao-Gui, Chen Tong, Liu Yan-Qin
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  • 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.
    • Funds:
    [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

  • [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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  • Received Date:  21 June 2010
  • Accepted Date:  02 August 2010
  • Published Online:  15 April 2011

Complexity evolvement of a chaotic fractional-orderfinancial system

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

Abstract: 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.

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