IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-96-5715-5_1.html

Crossing and Product Polynomial Systems

In: Two-dimensional Crossing and Product Polynomial Systems

Author

Listed:
  • Albert C. J. Luo

    (Southern Illinois University Edwardsville, Department of Mechanical and Mechatronics Engineering)

Abstract

In this chapter, the dynamics of crossing and product polynomial systems will be presented through a theorem. The singular equilibriums and 1-dimensional flows with infinite-equilibriums in product polynomial systems are presented in the theorem. The singular equilibriums are singular saddles and centers, parabola-saddles and inflections-saddles. The singular 1-dimensional flows are singular hyperbolic-flows, hyperbolic-to-hyperbolic-secant flows, inflection-source and sink flows, inflection-saddle flows. The corresponding first integral manifolds are obtained. The hybrid networks of singular equilibriums and 1-dimensional flows in the crossing and product polynomial systems are discussed in the theorem, and the corresponding infinite-equilibriums are given for switching bifurcations. The hybrid network of simple equilibriums and 1-dimensional flows with infinite-equilibriums in the crossing and product polynomial systems is stated in the theorem. The appearing and switching bifurcations of simple and singular 1-dimensional flows and equilibriums are stated in the theorem. Finally, the switching bifurcations of hybrid networks of simple and singular equilibriums and flows is also stated. The corresponding dynamical behaviors are presented through the following theorem.

Suggested Citation

  • Albert C. J. Luo, 2026. "Crossing and Product Polynomial Systems," Springer Books, in: Two-dimensional Crossing and Product Polynomial Systems, chapter 0, pages 1-125, Springer.
    • Handle: RePEc:spr:sprchp:978-981-96-5715-5_1
    DOI: 10.1007/978-981-96-5715-5_1
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    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:spr:sprchp:978-981-96-5715-5_1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.