Phase transitions and Lyapunov analysis of a heterogeneous traffic model involving human-driven and connected autonomous vehicles integrating overtaking effect

Abstract

In today's society, the intelligent connected vehicles technology is becoming the core driving force which leads the innovation of the transportation system. In actual traffic environments, when overtaking, in order to prevent rear end collisions, the front car often follows a backward looking behaviors for human-driven vehicles (HVs). To investigate the influence of overtaking effect and the backward looking effect in the connected autonomous vehicles (CAVs) environment, we innovatively propose a heterogeneous lattice hydrodynamics (LH) model that includes CAVs and HVs. Through linear stability analysis, we reveal the neutral stability condition and observe the expanding stable range owing to raising the penetration proportion of CAVs and the backward looking effect of HVs, and reducing the overtaking coefficient. On this basis, the nonlinear analysis is carried out to derive the modified mKdV equation successfully and reveal the kink-antikink soliton solution. The simulation results further confirm that the area of the density difference map is significantly reduced, and the stability of traffic flow is signally improved with the increase of the penetration proportion of CAVs and the backward looking effect of HVs and with the decrease of overtaking coefficient. In addition, with the help of the Lyapunov stability theory, we calculate the Lyapunov exponent and draw the density distribution to deeply investigate the chaos arising from overtaking effect for the new heterogeneous LH model, as well as the specific influence of overtaking effect on CAVs and the backward looking effect of HVs. Intelligent transportation system, as a multidisciplinary field, covers many disciplines such as traffic engineering, computer science, artificial intelligence, etc. Our research not only builds a new bridge for the cooperation between these disciplines, but also promotes the in-depth development of interdisciplinary research.