IDEAS home Printed from https://ideas.repec.org/a/hin/complx/6715036.html
   My bibliography  Save this article

Hopf Bifurcation and Chaos of a Delayed Finance System

Author

Listed:
  • Xuebing Zhang
  • Honglan Zhu

Abstract

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

Suggested Citation

  • Xuebing Zhang & Honglan Zhu, 2019. "Hopf Bifurcation and Chaos of a Delayed Finance System," Complexity, Hindawi, vol. 2019, pages 1-18, January.
    • Handle: RePEc:hin:complx:6715036
    DOI: 10.1155/2019/6715036
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2019/6715036.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2019/6715036.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/6715036?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yingkang Xie & Zhen Wang & Bo Meng, 2019. "Stability and Bifurcation of a Delayed Time-Fractional Order Business Cycle Model with a General Liquidity Preference Function and Investment Function," Mathematics, MDPI, vol. 7(9), pages 1-10, September.
    2. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    3. Vsevolod G. Sorokin & Andrei V. Vyazmin, 2022. "Nonlinear Reaction–Diffusion Equations with Delay: Partial Survey, Exact Solutions, Test Problems, and Numerical Integration," Mathematics, MDPI, vol. 10(11), pages 1-39, May.
    4. Zhang, Zizhen & Kundu, Soumen & Tripathi, Jai Prakash & Bugalia, Sarita, 2020. "Stability and Hopf bifurcation analysis of an SVEIR epidemic model with vaccination and multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Zizhen Zhang & Fangfang Yang & Wanjun Xia, 2019. "Hopf Bifurcation Analysis of a Synthetic Drug Transmission Model with Time Delays," Complexity, Hindawi, vol. 2019, pages 1-17, November.
    6. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Exact Solutions of Reaction–Diffusion PDEs with Anisotropic Time Delay," Mathematics, MDPI, vol. 11(14), pages 1-19, July.
    7. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    8. Dai, Qinrui & Rong, Mengjie & Zhang, Ren, 2022. "Bifurcations and multistability in a virotherapy model with two time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 289-311.
    9. 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.
    10. Andrei D. Polyanin & Vsevolod G. Sorokin, 2023. "Reductions and Exact Solutions of Nonlinear Wave-Type PDEs with Proportional and More Complex Delays," Mathematics, MDPI, vol. 11(3), pages 1-25, January.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:6715036. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.