Analysis Of The Stability And Solitary Waves For Two Types Of Car Following Model With Time Delays

With the development of high-tech, time delay’s effects become one of the keyfactors in the process for solving actual problems. In recent years, time delay’s effectson traffic flow are widely paid attentions by the relevant experts and scholars in thefield. In the traffic flow to the car following models, time delay’s effects are notnegligible influence on traffic flow due to driver’s reaction of time delay andmechanical delay.In this dissertation, time delays are introduced to the car-following model, thestability analysis and the reductive perturbation method are applied to obtain moreideal result. The specific work is given as follows:Firstly, we introduce asymmetric full velocity difference traffic model with a timedelay. By using the linear stability theory, stability conditions are obtained. By usingthe reductive perturbation method, the nonlinear density wave equation is derived.Moreover, we describe the nonlinear dynamic characteristics by using the solitarywave of these equations of the model.Secondly, assuming the same response to driver’s delay space headway andvelocity difference conditions, we introduce the multiple velocity difference trafficmodel with two same time delays. By using the linear stability theory, stabilityconditions are obtained in a wider range. By using the reductive perturbation method,the nonlinear density wave equation is derived. Moreover, we describe the nonlineardynamic characteristics by using the solitary wave of these equations of the model.Finally, assuming different reactions to the driver delay space headway andvelocity difference condition, we introduce a multiple velocity difference trafficmodel with two delays. By using the reductive perturbation method, the nonlineardensity wave equation is derived. Moreover, we describe the nonlinear dynamiccharacteristics by using the solitary wave of these equations of the model.