An extended car-following model with the dynamical collaborative between two consecutive vehicles

Abstract

An extended car-following model is proposed in this paper based on the idea of the dynamical cooperation between nearest-neighbor vehicles. The stability condition of the new model is derived by using the linear stability theory. By using the reductive perturbation method and nonlinear analysis, the modified Korteweg-de Vries (mKdV) equation are derived to describe the traffic density waves in the unstable region. And the corresponding kink-antikink solution is used to describe the traffic congestions. It is found that the dynamical collaboration between two consecutive vehicles can further stabilize traffic flow and suppress traffic jams effectively, which is verified by direct numerical simulations.