IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v37y2008i4p1104-1112.html
   My bibliography  Save this article

The inherent complexity in nonlinear business cycle model in resonance

Author

Listed:
  • Ma, Junhai
  • Sun, Tao
  • Liu, Lixia

Abstract

Based on Abraham C.-L. Chian’s research, we applied nonlinear dynamic system theory to study the first-order and second-order approximate solutions to one category of the nonlinear business cycle model in resonance condition. We have also analyzed the relation between amplitude and phase of second-order approximate solutions as well as the relation between outer excitements’ amplitude, frequency approximate solutions, and system bifurcation parameters. Then we studied the system quasi-periodical solutions, annulus periodical solutions and the path leading to system bifurcation and chaotic state with different parameter combinations. Finally, we conducted some numerical simulations for various complicated circumstances. Therefore this research will lay solid foundation for detecting the complexity of business cycles and systems in the future.

Suggested Citation

  • Ma, Junhai & Sun, Tao & Liu, Lixia, 2008. "The inherent complexity in nonlinear business cycle model in resonance," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1104-1112.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:4:p:1104-1112
    DOI: 10.1016/j.chaos.2006.10.013
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906009726
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.10.013?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chian, Abraham C.-L. & Borotto, Felix A. & Rempel, Erico L. & Rogers, Colin, 2005. "Attractor merging crisis in chaotic business cycles," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 869-875.
    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. 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. Mulligan, Robert F., 2010. "A fractal comparison of real and Austrian business cycle models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2244-2267.

    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. Mulligan, Robert F., 2010. "A fractal comparison of real and Austrian business cycle models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(11), pages 2244-2267.
    2. Elliott, Robert J. & Chen, Zhiping & Duan, Qihong, 2009. "Insurance claims modulated by a hidden Brownian marked point process," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 163-172, October.
    3. A. C. -L. Chian & E. L. Rempel & C. Rogers, 2007. "Crisis-induced intermittency in non-linear economic cycles," Applied Economics Letters, Taylor & Francis Journals, vol. 14(3), pages 211-218.
    4. 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.
    5. Valls, Claudia, 2012. "Rational integrability of a nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 141-146.
    6. Saiki, Y. & Chian, A.C.L. & Yoshida, H., 2011. "Economic intermittency in a two-country model of business cycles coupled by investment," Chaos, Solitons & Fractals, Elsevier, vol. 44(6), pages 418-428.
    7. Solari, Hernán G. & Natiello, Mario A., 2009. "The topological reconstruction of forced oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2023-2034.
    8. Li, Jiaorui & Feng, C.S., 2010. "First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5557-5562.
    9. António M Lopes & J A Tenreiro Machado & John S Huffstot & Maria Eugénia Mata, 2018. "Dynamical analysis of the global business-cycle synchronization," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-25, February.
    10. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    11. Ma, Junhai & Cui, Yaqiang & Liulixia,, 2009. "A study on the complexity of a business cycle model with great excitements in non-resonant condition," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2258-2267.
    12. 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.
    13. 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.
    14. Volos, Ch. K. & Kyprianidis, I.M. & Stouboulos, I.N. & Vaidyanathan, S. & Pham, V.-T., 2016. "Analysis, adaptive control and circuit simulation of a novel nonlinear finance systemAuthor-Name: Tacha, O.I," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 200-217.
    15. Chen, Juhn-Horng & Chen, Wei-Ching, 2008. "Chaotic dynamics of the fractionally damped van der Pol equation," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 188-198.

    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:eee:chsofr:v:37:y:2008:i:4:p:1104-1112. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.