Distributional chaos for the Forward and Backward Control traffic model

The interest in car-following models has increased in the last years due to its connection with vehicle-to-vehicle communications and the development of driverless cars. Some non-linear models such as the Gazes-Herman-Rothery model were already known to be chaotic. We consider the linear Forward and Backward Control traffic model for an infinite number of cars on a track. We show the existence of solutions with a chaotic behaviour by using some results of linear dynamics of C0-semigroups. In contrast, we also analyse which initial configurations lead to stable solutions.