Stduy Of Bifurcation And Chaos Based On The Car-following Models In Traffic Flow

The purpose of this dissertation is to analyze the non-linear dynamic behaviors in the car-following models for the fundamental mechanism that lies in the various non-linear phenomena.From order to disorder and then disorder to order reflects the typical aspect of the traffic flow. The traffic flow might march into a chaos during the transformation process under certain conditions, which has been proved by many scholars from different angles. The dissertation carefully studies the achievements made so far in the field from both home and abroad only to find that, there's a lack of the studies on the mechanism of the chaos in the traffic flow. Choosing the introduction of bifurcation theory into traffic chaos study as the breakthrough point, the stability in the traffic flow was studied and the results shows that the bifurcation phenomena incurred by the loss of stability in the traffic flow. The different scenarios for the transformation from bifurcation to chaos were further analyzed. the complicacy of chaos occurrence was explained.The main contents of the dissertation are as follows:The conditions for the stability of traffic flow were analyzed by the non-linear theory in the stimulus-response model and optimal velocity model. briefly covers the three-phase traffic flow theory, and through the simulation of transformation between different states of traffic flows, with the conditions of stability considered, the variety of the states of traffic flows was illustrated and the coexistence of continued-discontinued phase transition was discussed.The bifurcation phenomena were discussed respectively in both the optimal velocity model with the delay parameters and that without the delay parameters. And with the theory of stability analysis for the non-linear system a critical inter-relation expression, in which all the parameters are valid when the Hopf bifurcation occurs, is worked out. On the basis of the delay differential equation theory, by the center manifold and through the calculation of normal form, a discriminant was deduced for the judgment of direction and stability of Hopf bifurcation. Meanwhile, an analysis of the impact of bifurcating on the states of traffic flows was conducted with the help of simulating software and a further exploration was made on the possibility of the further transformation to chaos from bifurcating. From the chaotic quality of the car-following behaviors, by quantitive and qualitative analysis, and based on the identification algorithm of chaos previously achieved, the algorithm, for the confirmation of the chaos in the traffic flows based on the analysis of the combined group characteristics, was presented, and with it considered, a study over the chaotic phenomenon in the optimal velocity model was made and the impact of the parameters of the model on the states of traffic flows was also under discussion.Based on the analysis of the chaos of the traffic flow model, with the theory of bifurcation considered, and through deduction and computer simulation, etc. an exploration was conducted for basic channels to chaos in the traffic flow model. A conclusion was drawn that the chaotic phenomena do occur in the traffic flow system under certain conditions with the parameters, which were incurred by such different scenarios as through the development of the bifurcation, Feigenbaum , Pomeau-Manneville and Ruelle-Takens-Newhouse scenarios...