Synchronization transition and traffic congestion in one-dimensional traffic model. (English) Zbl 1351.90073

Xin, Zhi; Xu, Jian

Abstr. Appl. Anal. 2015, Article ID 167430, 10 p. (2015).

Summary: A nonlinear car-following model with driver’s reaction time is studied from the synchronization transition viewpoint. We investigate the traffic congestion from the view of chaos system synchronization transition. Our result shows that the uniform flow corresponds to the complete synchronization and the stop-and-go congested state corresponds to the lag synchronization of the vehicles. An analytical criterion for synchronization manifolds stability is obtained; the analytical result and the numerical result are consistent. The synchronization transition is also trigged by the driver’s reaction time. We analyze the car-following model by the use of the nonlinear analysis method and derive the modified KdV equation describing the kink density wave.

MSC:

90B20

Traffic problems in operations research

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