Density waves in car-following model for autonomous vehicles with backward looking effect.

• A novel car-following model is put forward to study the impact of backward looking effect on autonomous vehicles flow. • The conditions for judging the stability of traffic flow of autonomous vehicles are obtained. • The Burgers, KdV and mKdV equations are derived based on the nonlinear analysis. • The simulation results are consistent with the theoretical analysis results. Autonomous vehicles can obtain abundant road traffic information and communicate with each other using intelligent transportation system. For the purpose of detecting the influence of backward looking effect on the traffic flow of autonomous vehicles and better providing driving decisions for autonomous vehicles, in this study, a novel car-following model is presented accounting for the backward looking effect on the basis of the two-velocity difference model. The stability condition of this novel model in autonomous vehicles flow is established by incorporating the linear stability theory. The Burgers equation, Korteweg-de Vries equation, and modified Korteweg-de Vries equation are inferred based on nonlinear analysis to describe triangular wave, soliton wave, and kink-antikink wave, corresponding to the stable, metastable, and unstable regions of autonomous vehicles flow separately. Subsequently, numerical simulation is performed, exhibiting that this novel model can strengthen the traffic flow stability of autonomous vehicles and simulate the above three different density waves of traffic flow. In addition, the numerical simulation also further verifies the accuracy of the theoretical analysis. [ABSTRACT FROM AUTHOR]