IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i4p1135-1147.html
   My bibliography  Save this article

Chaos and its control in an impulsive differential system

Author

Listed:
  • Jiang, Guirong
  • Lu, Qishao
  • Qian, Linning

Abstract

In this paper, the existence of chaos and its control in an autonomous impulsive differential system are discussed both theoretically and numerically. The existence of a snap-back repeller, as well as the chaos in the sense of Li–Yorke, is proved based on the qualitative analysis using the Poincaré map and the Lambert W-function. Moreover, the existence of the period-3 periodic window embedded in the chaotic region is also demonstrated. An algorithm of chaos control to stabilize the unstable periodic solutions is proposed. Detailed numerical results of chaotic attractors and stabilization of unstable periodic orbits by the impulsive effects, which are illustrated by an example, are in good agreement with the theoretical analysis.

Suggested Citation

  • Jiang, Guirong & Lu, Qishao & Qian, Linning, 2007. "Chaos and its control in an impulsive differential system," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1135-1147.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:4:p:1135-1147
    DOI: 10.1016/j.chaos.2006.04.024
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906003456
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.04.024?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. Zhao, Zhong & Kong, Yinchang & Chen, Ying, 2016. "Dynamic analysis of the ethanol fermentation with the impulsive state feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 274-281.
    2. Xingjie Wu & Wei Du & Genan Pan & Wentao Huang, 2013. "The dynamical behaviors of a Ivlev-type two-prey two-predator system with impulsive effect," Indian Journal of Pure and Applied Mathematics, Springer, vol. 44(1), pages 1-27, February.

    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:34:y:2007:i:4:p:1135-1147. 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.