A macroscopic traffic flow model based on car-following models of aggressive and timid drivers is presented in this study. Utilizing differential equation theory, we derive the types and stability characteristics of equilibrium solutions across diverse scenarios within the model. The incorporation of a viscous component improves the system’s stability. Additionally, a branch analysis is performed on the new model to examine the emergence of Hopf and saddle-node bifurcations. Simulation results confirm that the proposed model accurately reflects intricate nonlinear phenomena in traffic flow. Notably, the numerical solutions obtained through data simulation align closely with analytical predictions. Additionally, our findings highlights the importance of incorporating branch analysis in providing complementary insights to existing traffic flow theories.
Yang et al. (Fri,) studied this question.