A Road Traffic Model with Overtaking: Continuation of the Oscillatory Patterns

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. In our previous work, we proposed a model which simulates an overtaking. The model implicitly defines a maneuver consisting of deceleration/acceleration just shortly before/after the overtaking. We observed a large variety of oscillatory solutions (oscillatory patterns) of the model. In case N = 3 (three cars on the route), we can supply a finite classification list of these patterns. In the present contribution, we stick to N = 3, and formulate our model as a particular Filippov system i.e., ODE with discontinuous righthand 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.