IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v82y2012i10p1874-1893.html
   My bibliography  Save this article

Continuation of oscillatory patterns in a road traffic model of three cars

Author

Listed:
  • Buřič, Lubor
  • Janovský, Vladimír

Abstract

We investigate microscopic models of the road traffic. In particular, we consider the car-following model for a single-line traffic flow of N identical cars on a circular road. The classical differentiable model breaks down at the time instant when two cars collide. Nevertheless, the natural action of a driver would be to overtake the slower car. In our previous work, we proposed the model which simulates overtaking. We observed a large variety of oscillatory solutions (oscillatory patterns) of the model. In the present contribution, we assume N=3 i.e., three cars on the route, and formulate our model as a particular piecewise smooth (PWS) dynamical system. We define generic oscillatory patterns as invariant objects of the flow defined by this PWS system. We use the standard software to continue the patterns with respect to a parameter (the length of the route). In this respect, we also investigate bifurcation phenomena.

Suggested Citation

  • Buřič, Lubor & Janovský, Vladimír, 2012. "Continuation of oscillatory patterns in a road traffic model of three cars," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(10), pages 1874-1893.
  • Handle: RePEc:eee:matcom:v:82:y:2012:i:10:p:1874-1893
    DOI: 10.1016/j.matcom.2011.07.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475411001674
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2011.07.001?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.

    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:82:y:2012:i:10:p:1874-1893. 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: 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.