One-parametric bifurcation analysis of data-driven car-following models

In this study, an equation-free method is used to perform bifurcation analyses of various artificial neural network (ANN) based car-following models. The ANN models were trained on Multiple Car Following (MCF) model output data (ANN-m) and field data (ANN-r). The ANN-m model could capture the behaviour of the MCF model in quite detail. A bifurcation analysis, using the circuit length L as parameter, for the ANN-m model leads to good results if the training data set from the MCF model is sufficiently diverse, namely that it incorporates data from a wide range of vehicle densities that encompass the stable free-flow and the stable jam-flow regimes. The ANN-r model is in general able to capture the feature of traffic jams when a car takes headway and velocity of itself and of the two cars ahead as input. However, the traffic flow of the ANN-r model is more regular in comparison to the field data. It is possible to construct a partial bifurcation diagram in L for the ANN-r using the equation-free method and it is found that the flow changes stability due to a subcritical Hopf bifurcation.