Barrachina, X.Conejero, J. A.Murillo Arcila, M.Seoane Sepúlveda, Juan Benigno2023-06-182023-06-182015-080024-379510.1016/j.laa.2015.04.010https://hdl.handle.net/20.500.14352/24100The 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.engjournal articlehttp://dx.doi.org/10.1016/j.laa.2015.04.010restricted access512Distributional chaosC0-semigroupDevaney-chaosBirth-and-death modelsCar-following modelsÁlgebra1201 Álgebra