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Phase Plane Analysis of Traffic Flow Evolution Based on Sticky Payne Model

In this paper, a new phase plane analysis method is proposed to study the nonlinear phenomena of traffic flow. This method transforms the traditional traffic flow model into a new improved model through variable substitution to adapt to the phase plane analysis. According to the improved model, the corresponding relationship between traffic congestion and system instability can be seen on the phase plan, which can be used for the stability analysis of various traffic flow phenomena. Thus, the problem of traffic flow is transformed into the problem of system stability.