IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/405639.html
   My bibliography  Save this article

Neimark-Sacker Bifurcation in a Discrete-Time Financial System

Author

Listed:
  • Baogui Xin
  • Tong Chen
  • Junhai Ma

Abstract

A discrete-time financial system is proposed by using forward Euler scheme. Based on explicit Neimark-Sacker bifurcation (also called Hopf bifurcation for map) criterion, normal form method and center manifold theory, the system's existence, stability and direction of Neimark-Sacker bifurcation are studied. Numerical simulations are employed to validate the main results of this work. Some comparison of bifurcation between the discrete-time financial system and its continuous-time system is given.

Suggested Citation

  • Baogui Xin & Tong Chen & Junhai Ma, 2010. "Neimark-Sacker Bifurcation in a Discrete-Time Financial System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-12, September.
    • Handle: RePEc:hin:jnddns:405639
    DOI: 10.1155/2010/405639
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2010/405639.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2010/405639.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2010/405639?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
    ---><---

    References listed on IDEAS

    as
    1. Chiarella,Carl & Flaschel,Peter, 2011. "The Dynamics of Keynesian Monetary Growth," Cambridge Books, Cambridge University Press, number 9780521180184, October.
    2. Wu, Wenjuan & Chen, Zengqiang & Yuan, Zhuzhi, 2009. "The evolution of a novel four-dimensional autonomous system: Among 3-torus, limit cycle, 2-torus, chaos and hyperchaos," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2340-2356.
    3. He, Xue-Zhong & Westerhoff, Frank H., 2005. "Commodity markets, price limiters and speculative price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1577-1596, September.
    4. Jess Benhabib & Kazuo Nishimura, 2012. "The Hopf Bifurcation and Existence and Stability of Closed Orbits in Multisector Models of Optimal Economic Growth," Springer Books, in: John Stachurski & Alain Venditti & Makoto Yano (ed.), Nonlinear Dynamics in Equilibrium Models, edition 127, chapter 0, pages 51-73, Springer.
    5. Xin, Baogui & Ma, Junhai & Gao, Qin, 2009. "The complexity of an investment competition dynamical model with imperfect information in a security market," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2425-2438.
    6. Nawrocki, David, 1984. "Entropy, Bifurcation and Dynamic Market Disequilibrium," The Financial Review, Eastern Finance Association, vol. 19(2), pages 266-284, May.
    7. Chiarella, Carl & He, Xue-Zhong & Hung, Hing & Zhu, Peiyuan, 2006. "An analysis of the cobweb model with boundedly rational heterogeneous producers," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 750-768, December.
    8. 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.
    9. Chian, Abraham C.-L. & Rempel, Erico L. & Rogers, Colin, 2006. "Complex economic dynamics: Chaotic saddle, crisis and intermittency," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1194-1218.
    10. Dowrick,Steve & Pitchford,Rohan & Turnovsky,Stephen J. (ed.), 2004. "Economic Growth and Macroeconomic Dynamics," Cambridge Books, Cambridge University Press, number 9780521835619, October.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    2. Blé, Gamaliel & Dela-Rosa, Miguel Angel, 2019. "Neimark–Sacker bifurcation in a tritrophic model with defense in the prey," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 124-139.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Datta, Soumya, 2013. "Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems," MPRA Paper 50814, University Library of Munich, Germany.
    2. William Barnett & Evgeniya Duzhak, 2010. "Empirical assessment of bifurcation regions within New Keynesian models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 99-128, October.
    3. Ding, Yuting & Jiang, Weihua & Wang, Hongbin, 2012. "Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1048-1057.
    4. Barnett, William A. & Duzhak, Evgeniya Aleksandrovna, 2008. "Non-robust dynamic inferences from macroeconometric models: Bifurcation stratification of confidence regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3817-3825.
    5. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Barnett, William A. & He, Susan, 2010. "Existence of singularity bifurcation in an Euler-equations model of the United States economy: Grandmont was right," Economic Modelling, Elsevier, vol. 27(6), pages 1345-1354, November.
    7. Barnett, William A. & Chen, Guo, 2015. "Bifurcation of Macroeconometric Models and Robustness of Dynamical Inferences," Foundations and Trends(R) in Econometrics, now publishers, vol. 8(1-2), pages 1-144, September.
    8. Murakami, Hiroki, 2020. "Monetary policy in the unique growth cycle of post Keynesian systems," Structural Change and Economic Dynamics, Elsevier, vol. 52(C), pages 39-49.
    9. 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.
    10. Stéphane Hallegatte & Michael Ghil, 2007. "Endogenous Business Cycles and the Economic Response to Exogenous Shocks," Working Papers 2007.20, Fondazione Eni Enrico Mattei.
    11. Barnett, William A. & Duzhak, Evgeniya A., 2019. "Structural Stability Of The Generalized Taylor Rule," Macroeconomic Dynamics, Cambridge University Press, vol. 23(4), pages 1664-1678, June.
    12. Maćkowiak, Piotr, 2009. "Adaptive Rolling Plans Are Good," MPRA Paper 42043, University Library of Munich, Germany.
    13. Heidari , Hassan & Refah-Kahriz, Arash & Hashemi Berenjabadi, Nayyer, 2018. "Dynamic Relationship between Macroeconomic Variables and Stock Return Volatility in Tehran Stock Exchange: Multivariate MS ARMA GARCH Approach," Quarterly Journal of Applied Theories of Economics, Faculty of Economics, Management and Business, University of Tabriz, vol. 5(2), pages 223-250, August.
    14. Vasco M. Carvalho & Alireza Tahbaz-Salehi, 2019. "Production Networks: A Primer," Annual Review of Economics, Annual Reviews, vol. 11(1), pages 635-663, August.
    15. Xin, Baogui & Ma, Junhai & Gao, Qin, 2009. "The complexity of an investment competition dynamical model with imperfect information in a security market," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2425-2438.
    16. Tarek Coury & Yi Wen, 2009. "Global indeterminacy in locally determinate real business cycle models," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 49-60, March.
    17. Krawiec, Adam & Szydłowski, Marek, 2017. "Economic growth cycles driven by investment delay," Economic Modelling, Elsevier, vol. 67(C), pages 175-183.
    18. Brito Paulo & Marini Giancarlo & Piergallini Alessandro, 2016. "House prices and monetary policy," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 20(3), pages 251-277, June.
    19. Gang Gong, 2005. "Modeling Stabilization Policies In A Financially Unstable Economy," Metroeconomica, Wiley Blackwell, vol. 56(3), pages 281-304, July.
    20. Michele Boldrin, 1988. "Persistent Oscillations and Chaos in Dynamic Economic Models: Notes for a Survey," UCLA Economics Working Papers 458A, UCLA Department of Economics.

    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:jnddns:405639. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.