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

  • Buřič L
  • Janovský V
  • 2

    Readers

    Mendeley users who have this article in their library.
  • 1

    Citations

    Citations of this article.

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. © 2011 IMACS. Published by Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Microscopic models
  • Overtaking
  • Path-following
  • Piecewise smooth dynamics
  • Road traffic

Get free article suggestions today

Mendeley saves you time finding and organizing research

Sign up here
Already have an account ?Sign in

Find this document

Authors

  • Lubor Buřič

  • Vladimír Janovský

Cite this document

Choose a citation style from the tabs below

Save time finding and organizing research with Mendeley

Sign up for free