IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v27y2006i5p1229-1238.html
   My bibliography  Save this article

Piecewise-linearized methods for oscillators with limit cycles

Author

Listed:
  • Ramos, J.I.

Abstract

A piecewise linearization method based on the linearization of nonlinear ordinary differential equations in small intervals, that provides piecewise analytical solutions in each interval and smooth solutions everywhere, is developed for the study of the limit cycles of smooth and non-smooth, conservative and non-conservative, nonlinear oscillators. It is shown that this method provides nonlinear maps for the displacement and velocity which depend on the previous values through the nonlinearity and its partial derivatives with respect to time, displacement and velocity, and yields non-standard finite difference formulae. It is also shown by means of five examples that the piecewise linearization method presented here is more robust and yields more accurate (in terms of displacement, energy and frequency) solutions than the harmonic balance procedure, the method of slowly varying amplitude and phase, and other non-standard finite difference equations.

Suggested Citation

  • Ramos, J.I., 2006. "Piecewise-linearized methods for oscillators with limit cycles," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1229-1238.
    • Handle: RePEc:eee:chsofr:v:27:y:2006:i:5:p:1229-1238
    DOI: 10.1016/j.chaos.2005.04.084
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077905004364
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2005.04.084?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.

    Citations

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


    Cited by:

    1. Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
    2. Ramos, J.I., 2006. "Determination of periodic orbits of nonlinear oscillators by means of piecewise-linearization methods," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1306-1313.
    3. Sun, Yeong-Jeu, 2009. "Existence of self-oscillation for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 731-734.
    4. Singh, Vimal, 2008. "Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 178-183.
    5. Sun, Yeong-Jeu, 2007. "Limit cycles design for a class of bilinear control systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 156-162.
    6. Singh, Vimal, 2007. "A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 813-816.
    7. Sun, Yeong-Jeu, 2009. "The existence of the exponentially stable limit cycle for a class of nonlinear systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2357-2362.
    8. Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
    9. Sun, Yeong-Jeu, 2008. "Existence and uniqueness of limit cycle for a class of nonlinear discrete-time systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 89-96.

    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:27:y:2006:i:5:p:1229-1238. 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: 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.