Abstract
We investigate microscopic models of the road traffic. In particular, we consider car-following models for a single-line traffic flow on a circular road.
The classical differentiable models break down at the time instant when two cars collide. Nevertheless, the natural action of a driver would be to overtake the slower car.
We propose a model which simulates an overtaking. The model implicitly defines a maneuver consisting of deceleration/acceleration just shortly before/after the overtaking.
We observe a large variety of oscillatory solutions (oscillatory patterns) of the model. In case of cars on the route, we can supply a finite classification list of these patterns.
In that case, we can formulate our model as a particular Filippov system i.e., ODE with discontinuous right-hand sides. We define oscillatory patterns as invariant objects of this Filippov system.
We use the standard software (AUTO97) to continue these patterns with respect to a parameter.