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 the overtaking. We observed a large variety of oscillatory solutions {oscillatory patterns) of the model.
In the present contribution, we formulate our model as a particular Filippov system i.e., ODEs with discontinuous righthand sides. Hence, we can identify our problem with a well defined solution class.
We define oscillatory patterns as invariant objects of this Filippov system.