IDEAS home Printed from https://ideas.repec.org/a/hin/jjmath/347071.html
   My bibliography  Save this article

Stability and Andronov-Hopf Bifurcation of a System with Three Time Delays

Author

Listed:
  • Svetoslav Nikolov

Abstract

A general system of three autonomous ordinary differential equations with three discrete time delays is considered. With respect to the delays, we investigate the local stability of equilibria by analyzing the corresponding characteristic equation. Using the Hopf bifurcation theorem, we predict the occurrence of a limit cycle bifurcation for the time delay parameters. Thus, some new mathematical results are obtained. Finally, the above mentioned criteria are applied to a system modelling miRNA regulation.

Suggested Citation

  • Svetoslav Nikolov, 2013. "Stability and Andronov-Hopf Bifurcation of a System with Three Time Delays," Journal of Mathematics, Hindawi, vol. 2013, pages 1-11, March.
    • Handle: RePEc:hin:jjmath:347071
    DOI: 10.1155/2013/347071
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/JMATH/2013/347071.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/JMATH/2013/347071.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/347071?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. Sipahi, Rifat & Delice, Ismail Ilker, 2010. "Stability of inventory dynamics in supply chains with three delays," International Journal of Production Economics, Elsevier, vol. 123(1), pages 107-117, January.
    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. Ivanov, Dmitry & Sokolov, Boris, 2013. "Control and system-theoretic identification of the supply chain dynamics domain for planning, analysis and adaptation of performance under uncertainty," European Journal of Operational Research, Elsevier, vol. 224(2), pages 313-323.
    2. Palsule-Desai, Omkar D. & Tirupati, Devanath & Chandra, Pankaj, 2013. "Stability issues in supply chain networks: Implications for coordination mechanisms," International Journal of Production Economics, Elsevier, vol. 142(1), pages 179-193.
    3. Lin, J. & Naim, M.M. & Purvis, L. & Gosling, J., 2017. "The extension and exploitation of the inventory and order based production control system archetype from 1982 to 2015," International Journal of Production Economics, Elsevier, vol. 194(C), pages 135-152.
    4. Lin, Junyi & Naim, Mohamed M. & Spiegler, Virginia L.M., 2020. "Delivery time dynamics in an assemble-to-order inventory and order based production control system," International Journal of Production Economics, Elsevier, vol. 223(C).
    5. Hill, Alex & Doran, Des & Stratton, Roy, 2012. "How should you stabilise your supply chains?," International Journal of Production Economics, Elsevier, vol. 135(2), pages 870-881.
    6. Chiang, Chung-Yean & Qian, Zhuang & Chuang, Chia-Hung & Tang, Xiao & Chou, Chia-Ching, 2023. "Examining demand and supply-chain antecedents of inventory dynamics: Evidence from automotive industry," International Journal of Production Economics, Elsevier, vol. 259(C).
    7. Fu, Lingxian & Meng, Fanyong, 2020. "A human disease transmission inspired dynamic model for closed-loop supply chain management," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).

    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:jjmath:347071. 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.