Chaotic jam and phase transitions in a lattice model with density dependent passing

In real traffic dynamics, passing has a significant impact on the traffic flow. Passing/Overtaking is primarily influenced by the traffic density in the surroundings, therefore considering passing as constant is impractical. In this paper, we proposed a lattice hydrodynamic model with the consideration of density dependent passing for a unidirectional single lane highway to examine the traffic system more realistically. Due to various experimental investigations, the passing behavior is considered similar to the flow-density curve. The passing increases with the density and after achieving a maximum at a critical value, it decreases. Thus, implementing the idea to model density dependent passing similar to the optimal velocity function. The impact of density dependent passing on the lattice model is investigated through linear stability analysis and it is shown that with an increase in passing, the stability region reduces significantly. Using nonlinear analysis, the kink-antikink solution of the mKdV equation is obtained to describe the propagating behavior of the density wave near the critical point. For the small values of passing, there is a phase transition from the kink jam region to the free flow region, with decreasing sensitivity. On the other hand, for large values of passing, the phase transition occurs from the uniform to the kink jam region through the chaotic jam region, with increasing delay time. The influence of parameters involved in density dependent passing is investigated theoretically as well as numerically.