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Control Strategy for a Fractional-Order Chaotic Financial Model

Author

Listed:
  • Changjin Xu
  • Maoxin Liao
  • Peiluan Li
  • Qimei Xiao
  • Shuai Yuan

Abstract

In this article, based on the previous works, a new fractional-order financial model is put up. The chaotic behavior of the fractional-order financial model is suppressed by designing an appropriate controller. By choosing the delay as the bifurcation parameter, we establish the sufficient condition to guarantee the stability and the existence of Hopf bifurcation of fractional-order financial model. Also, the influence of the delay and the fractional order on the stability and the existence of Hopf bifurcation of fractional-order financial model is revealed. An example is given to confirm the effectiveness of the analysis results. The main findings of this article play an important role in maintaining economic stability.

Suggested Citation

  • Changjin Xu & Maoxin Liao & Peiluan Li & Qimei Xiao & Shuai Yuan, 2019. "Control Strategy for a Fractional-Order Chaotic Financial Model," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    • Handle: RePEc:hin:complx:2989204
    DOI: 10.1155/2019/2989204
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    References listed on IDEAS

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    1. Son, Woo-Sik & Park, Young-Jai, 2011. "Delayed feedback on the dynamical model of a financial system," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 208-217.
    2. Apostolos Serletis, 1996. "Is There Chaos in Economic Time Series?," Canadian Journal of Economics, Canadian Economics Association, vol. 29(s1), pages 210-212, April.
    3. Rongyan Zhang, 2012. "Bifurcation Analysis for a Kind of Nonlinear Finance System with Delayed Feedback and Its Application to Control of Chaos," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-18, April.
    4. Huang, Chengdai & Cai, Liming & Cao, Jinde, 2018. "Linear control for synchronization of a fractional-order time-delayed chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 326-332.
    5. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    6. Xuebing Zhang & Honglan Zhu, 2019. "Hopf Bifurcation and Chaos of a Delayed Finance System," Complexity, Hindawi, vol. 2019, pages 1-18, January.
    7. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    8. Yiding Yue & Lei He & Guanchun Liu, 2013. "Modeling and Application of a New Nonlinear Fractional Financial Model," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, November.
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    Cited by:

    1. Sweilam, N.H. & AL - Mekhlafi, S.M. & Mohamed, D.G., 2021. "Novel chaotic systems with fractional differential operators: Numerical approaches," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

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