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

Highlights

• Bifurcation diagrams are computed from experimental data using machine learning.

• A Bautin bifurcation underlies the macroscopic behaviour of the traffic flow.

• Car-following models capture the essential physics of traffic flow.

Abstract

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.