IDEAS home Printed from https://ideas.repec.org/a/hin/jnddns/160672.html
   My bibliography  Save this article

Basin of Attraction through Invariant Curves and Dominant Functions

Author

Listed:
  • Ziyad AlSharawi
  • Asma Al-Ghassani
  • A. M. Amleh

Abstract

We study a second-order difference equation of the form , where both and are decreasing. We consider a set of invariant curves at and use it to characterize the behaviour of solutions when and when . The case is related to the Y2K problem. For , we study the stability of the equilibrium solutions and find an invariant region where solutions are attracted to the stable equilibrium. In particular, for certain range of the parameters, a subset of the basin of attraction of the stable equilibrium is achieved by bounding positive solutions using the iteration of dominant functions with attracting equilibria.

Suggested Citation

  • Ziyad AlSharawi & Asma Al-Ghassani & A. M. Amleh, 2015. "Basin of Attraction through Invariant Curves and Dominant Functions," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-11, May.
    • Handle: RePEc:hin:jnddns:160672
    DOI: 10.1155/2015/160672
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/DDNS/2015/160672.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/DDNS/2015/160672.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/160672?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
    ---><---

    References listed on IDEAS

    as
    1. Abu-Saris, Raghib & AlSharawi, Ziyad & Rhouma, Mohamed Ben Haj, 2013. "The dynamics of some discrete models with delay under the effect of constant yield harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 54(C), pages 26-38.
    2. Ziyad AlSharawi, 2013. "A Global Attractor in Some Discrete Contest Competition Models with Delay under the Effect of Periodic Stocking," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, October.
    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. Zhang, Limin & Zhang, Chaofeng & Zhao, Min, 2014. "Dynamic complexities in a discrete predator–prey system with lower critical point for the prey," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 105(C), pages 119-131.

    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:hin:jnddns:160672. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.