Researches On Solitary Waves Of Optimal Velocity Model With Fractional Or Intelligent Information

In recent years,the research on fractional order system has been gained wide attention,but there is no research work in the field of traffic flow.The intelligent transportation system formed by applications of intelligent technology system is changing the pattern of traffic field.Therefore,it is significant to study traffic flow model with fractional or intelligent information.In this dissertation,a definition of fractional order or intelligent information is introduced into the optimal velocity model to give three optimal velocity models with fractional order or intelligent information.The stability and solitary waves of them are studied.The obtained concrete results are as follows:Firstly,for the introduced fractional optimal velocity model,the stability condition according to the linear stability analysis is obtained.It is found that the stable region is larger than that of the integer order optimal velocity model.Then,by analyzing the model with the nonlinear method of perturbation,Burgers equation,mKdV equation and KdV equation are derived respectively in the corresponding stable,unstable and meta-stable regions.The corresponding kink solution and solitary wave solution of vehicle pitch and the number of vehicles are given.Furthermore,the influences of the model on traffic flow problems are analyzed.Secondly,by considering the driver's time delay to the vehicle distance in the fractional optimal velocity model,a fractional optimal velocity model with time delay is given.The stability condition of the model is derived.It is shown that its stable region is larger than that of the fractional optimal velocity model without time delay.By analyzing the model with the nonlinear method of perturbation,the corresponding nonlinear wave equations are derived respectively in stable,unstable and meta-stable regions.The solitary wave solutions in corresponding regions are given.Finally,by considering the intelligent information in the fractional optimal velocity model,a fractional optimal velocity model with intelligent information is given.The stability condition of the model is derived.It is shown that the stable region of fractional optimal velocity model with intelligent information is larger than that of the fractional optimal velocity model.By analyzing the model with the nonlinear method of perturbation,the corresponding nonlinear wave equations are derived respectively in stable,unstable and meta-stable regions.The kink solution and solitary wavesolutions of vehicle pitch and the number of vehicles in the corresponding regions are given.The influences of intelligent information on the traffic flow model are analyzed.