Nonlinear analysis of a new car-following model accounting for the optimal velocity changes with memory

• A new car-following model is proposed by accounting for the optimal velocity changes with memory.
• The impact of optimal velocity changes with memory on the stability of traffic flow is identified.
• Nonlinear analysis of mKdV equation is investigated considering the optimal velocity changes with memory.
• Numerical results show that the optimal velocity changes with memory greatly affect car-following behaviors.

We, in this study, construct a new car-following model by accounting for the effect of the optimal velocity changes with memory in terms of the full velocity difference (FVD) model. The stability condition and mKdV equation concerning the optimal velocity changes with memory are derived through both linear stability and nonlinear analyses, respectively. Then, the space concerned can be divided into three regions classified as the stable, the metastable and the unstable ones. Moreover, it is shown that the effect of the optimal velocity changes with memory could enhance the stability of traffic flow. Furthermore, the numerical results verify that not only the sensitivity parameter of the optimal velocity changes with memory of driver but also the memory step could effectively stabilize the traffic flow. In addition, the stability of traffic flow is strengthened by increasing the memory step-size of optimal velocity changes and the intensity of drivers’ memory with such changes. Most importantly, the effect of the optimal velocity changes with memory may avoid the disadvantage of historical information, which decreases the stability of traffic flow on road.