## 7 Discussion  
Understanding the formatting condition and the evolution mechanism is crucial for alleviating and suppressing traffic congestion, as well as for improving communities' traffic efficiency. The stability analysis of car-following models is a key means to achieve this understanding. Under the conditions of penetration of CAV technologies, such as V2X, vehicles and drivers can access the motion state information of the SLV along with the rear vehicle within the current lane and apply it to the car-following behavior. However, there is currently no model that comprehensively incorporates the SLV and the \"looking backward effect\", which limits the understanding of characteristics of the car-following behavior and traffic flow under the corresponding condition. Motivated by these, an extended car-following model with consideration of the SLV and the rear vehicle was established in this work to study the linear stability and nonlinear characteristics of traffic flow. In Sections 3 and 4, the linear stability and nonlinear analysis were carried out, respectively, utilizing the linear stability analysis method and reductive perturbation method, and the neutral stability condition and mKdV equation, as well as its solution, were derived. According to these efforts, the neutral stability curves and the coexisting curves in the headway-sensitivity phase space were conducted, as shown in Figure 1. The impact of sensitivity on stability was also discussed, as shown in Figures 2 and 3. In Figure 1, we can see that the area, which is enclosed by the neutral stability curves and the X-axis, of the SLVRV model is smaller than that of the FVD, BLVD,  
Figure 6: Space–time evolution of the headway after \(t=14,800\) s. (The patterns **(a–d)** are for the coexisting phases corresponding to the four models). and SLV models, which reveals that the stability of traffic flow with the SLVRV model is enhanced by considering the motion state information of the SLV and the rear vehicle. As shown in Figures 2 and 3, the stability continued to be enhanced as the drivers paid more attention to the SLV or the rear vehicle. These results suggest that while paying attention to the headway and velocity difference between the vehicle and its front vehicle, paying more attention to the motion state of the SLV and the rear vehicle will assist the driver with a better understanding of the surrounding traffic conditions. Particularly, the motion state of the SLV can help the driver better grasp the traffic condition of the road rather than of the current lane. With a better understanding of the traffic condition, drivers can adjust and optimize their car-following behavior, and thus the stability of traffic flow will be enhanced. Below the stable region, there are metastable regions and the unstable region, as shown in Figure 1. The traffic flow is about to become unstable in the metastable region and has become unstable, which will lead to traffic jams, in the unstable region. Traffic congestion, which is essentially an extreme case in the propagation of density waves, is one of the most common and important complexes and nonlinear phenomena in traffic flow. When the traffic flow becomes unstable, the density wave propagates in the form of a kink-antikink wave. The propagation characteristics, which express the operation characteristics of traffic flow when it becomes unstable, including the selected velocity \(c\) and the amplitude \(A\) of the wave, can be described with the corresponding equations in Section 4. To verify the aforementioned results of the theoretical analysis and further investigate the operation and evolution characteristics of traffic flow with consideration of the motion state information of the SLV and the rear vehicle under the conditions of the penetration of CAV technologies, such as V2X, a scenario about the disturbance propagation was constructed, and then numerical simulation on the disturbance propagation in the vehicles system was conducted.