IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v81y2011i11p2549-2563.html
   My bibliography  Save this article

Generating chaotic attractors on a surface

Author

Listed:
  • Morel, C.
  • Vlad, R.
  • Morel, J.-Y.
  • Petreus, D.

Abstract

The present paper introduces a new method to generate several independent periodic attractors, based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on an arbitrarily precise zone of a paraboloid or plane. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced.

Suggested Citation

  • Morel, C. & Vlad, R. & Morel, J.-Y. & Petreus, D., 2011. "Generating chaotic attractors on a surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2549-2563.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:11:p:2549-2563
    DOI: 10.1016/j.matcom.2011.05.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411001157
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2011.05.003?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. Morel, Cristina & Bourcerie, Marc & Chapeau-Blondeau, François, 2005. "Generating independent chaotic attractors by chaos anticontrol in nonlinear circuits," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 541-549.
    2. Peng, Mingshu, 2005. "Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1287-1297.
    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. Morel, C. & Morel, J.-Y. & Danca, M.F., 2018. "Generalization of the Filippov method for systems with a large periodic input," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 1-13.
    2. Pham, Viet–Thanh & Jafari, Sajad & Volos, Christos & Kapitaniak, Tomasz, 2016. "A gallery of chaotic systems with an infinite number of equilibrium points," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 58-63.

    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. Peng, Mingshu & Yuan, Yuan, 2008. "Complex dynamics in discrete delayed models with D4 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 393-408.
    2. Attili, Basem S., 2009. "A direct method for the numerical computation of bifurcation points underlying symmetries," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1545-1551.

    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:matcom:v:81:y:2011:i:11:p:2549-2563. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.