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.
