Dynamics Of The Optimal Velocity Car-following Models With State-dependent Reaction Time Delays

The traffic dynamics is a very complex nonlinear problem. Time delay has in-dispensable influence on it. Supported by the National Natural Science Foundation of China(NO.11372282), this dissertation mostly investigate bifurcations of the op-timal velocity three cars car-following models with state-dependent time delay on a loop lane and a straight lane. In this dissertation, firstly, approximation formula of reaction time delay is established under a certain assumptions proposed in the the-ory of the car-following models. Then the optimal velocity three cars car-following models on a loop lane and a straight lane with this formula of reaction time delay are built up. For the model on the straight lane, employing the bifurcation analysis software DDE-BIFTOOL of the delayed dynamics, the bifurcation analysis is exe-cuted by taking vq,v as the bifurcation parameters. The results display the traffic flow can produce stable periodic oscillation after the uniform flow loses its stability, i.e., free flow becomes congestion flow. For the model on the loop lane, choosing s,vq as the bifurcation parameters, the characteristic equation is obtained by the formal linearization. As 0 is always the root of the characteristic equation, the usual bifurcation analysis can not be executed. But we can investigate the bifurcation in the complementary space of center subspace. The results imply that the Hopf bifur-cation can appear in this system. The numerical simulations reveal that the traffic flow can produce subcritical bifurcation in the neighborhood of the critical value, i.e., the traffic How can take birth to unstable periodic oscillation and be stop-and-go after the uniform flow loses its stability.The features and the innovation of this dissertation are the following:differ-ent from that the reaction time delay is constant in the previous study, the state-dependent reaction time delay but not constant is introduced into the traffic dynam-ics models. At the first time, the approximate formula of the reaction time delay is established and its state-dependency is proved. For the translational symmetric system with 0 characteristic root, we can transfer the Hopf bifurcation analysis into that in the complementary space of center subspace.