Modeling of Flow-Difference Influences on Dynamic Phase Transition and Stability in Curved Road Traffic Systems

The traffic flow difference factor is of great significance for traffic flow stability and congestion mitigation. However, its role has not been studied in existing curved-road traffic flow models. To fill this gap, this study proposes an improved lattice traffic flow model for curved roads based on lattice hydrodynamic theory, which comprehensively considers the synergistic influence of curve geometric characteristics and the flow difference factor on traffic dynamics. Meanwhile, the new model adopts a modified optimal speed function regarding the symmetric characteristics of density. Through linear stability analysis, the stability criterion of the new model is derived. Via nonlinear analysis, the mKdV equation describing the propagation mechanism of traffic congestion near the critical point, along with its density wave solution, is obtained. The results show that introducing the traffic flow difference factor can significantly suppress the propagation speed and fluctuation amplitude of density waves and reduce the driver’s critical sensitivity coefficient, thereby effectively enhancing the stability and robustness of traffic flow on curved roads. Moreover, the model’s stability gradually improves as the curve curvature increases. Under the same curve conditions, compared with the classical Zhou model, the critical sensitivity and density wave propagation speed of the new model are reduced by approximately 16.67% and 19.48%, respectively, with favorable traffic congestion suppression effects.