IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i4p2023-2034.html
   My bibliography  Save this article

The topological reconstruction of forced oscillators

Author

Listed:
  • Solari, Hernán G.
  • Natiello, Mario A.

Abstract

Periodically forced oscillators are among the simplest dynamical systems capable to display chaos. They can be described by the variables position and velocity, together with the phase of the force. Their phase-space corresponds therefore to R2×S1. The organization of the periodic orbits can be displayed with braids having only positive crossings. Topological characterization of dynamical systems actually began to be explored in physics on this family of problems.

Suggested Citation

  • Solari, Hernán G. & Natiello, Mario A., 2009. "The topological reconstruction of forced oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2023-2034.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:4:p:2023-2034
    DOI: 10.1016/j.chaos.2009.03.167
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909003166
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.03.167?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. Stavrinides, S.G. & Deliolanis, N.C. & Laopoulos, Th. & Kyprianidis, I.M. & Miliou, A.N. & Anagnostopoulos, A.N., 2008. "The intermittent behavior of a second-order non-linear non-autonomous oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1191-1199.
    2. Gan, Chunbiao & He, Shimin, 2008. "Surrogate test for noise-contaminated dynamics in the Duffing oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1517-1522.
    3. 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.
    4. Rusinek, Rafal & Warminski, Jerzy, 2009. "Attractor reconstruction of self-excited mechanical systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 172-182.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    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. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    2. Valls, Claudia, 2012. "Rational integrability of a nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 141-146.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Dominique Guégan & Justin Leroux, 2008. "Local Lyapunov exponents: Zero plays no role in Forecasting chaotic systems," Cahiers de recherche 08-10, HEC Montréal, Institut d'économie appliquée.
    9. Richter, Hendrik, 2008. "On a family of maps with multiple chaotic attractors," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 559-571.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Dominique Guegan & Justin Leroux, 2009. "Forecasting chaotic systems: The role of local Lyapunov exponents," PSE-Ecole d'économie de Paris (Postprint) halshs-00431726, HAL.
    15. Chagas, T.P. & Toledo, B.A. & Rempel, E.L. & Chian, A.C.-L. & Valdivia, J.A., 2012. "Optimal feedback control of the forced van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1147-1156.
    16. Vasily E. Tarasov, 2019. "Rules for Fractional-Dynamic Generalizations: Difficulties of Constructing Fractional Dynamic Models," Mathematics, MDPI, vol. 7(6), pages 1-50, June.
    17. Li, Jiaorui & Ren, Zhengzheng & Wang, Zuoren, 2008. "Response of nonlinear random business cycle model with time delay state feedback," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(23), pages 5844-5851.
    18. 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.
    19. 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.
    20. Dominique Guegan & Justin Leroux, 2009. "Forecasting chaotic systems: The role of local Lyapunov exponents," Post-Print halshs-00431726, HAL.

    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:42:y:2009:i:4:p:2023-2034. 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.