Publication at Faculty of Mathematics and Physics |
2009
Abstract
The classical microscopic single line follow-the-leader model of a road traffic may collapse in finite time due to a car collision. In order to avoid the collision, the natural action of a driver would be to overtake the slower car.
We propose a simple model of overtaking assuming a circular road. The model is a dynamical system with discontinuous right-hand side (the Filippov system).
As a case study, we assumed that the system consists of N = 3 identical cars. We studied a particular periodic solution (oscillatory pattern).
We explored the possibility to use the standard software (AUTO97) to continue the pattern with respect to a parameter.
