两类含时滞跟驰模型的稳定性和孤立波分析
发布时间：2018-09-06 10:27
【摘要】：随着各种高新技术的发展,时滞效应在解决实际问题的过程中成为关键因素之一.近年来,时滞效应对交通流的影响受到各相关领域专家学者的广泛关注.在交通流跟驰模型中,由于司机反应时滞以及机械时滞,对交通流的影响是不可忽略的. 本文将时滞引入到跟驰模型中,运用稳定性分析和约化摄动法分析获得了比较理想的结果.具体工作如下: 首先,引入含时滞不对称全速度差交通流模型,运用线性稳定性分析得到稳定性条件,通过约化摄动法分析此模型的非线性动力学特征:在稳定流区域,推导出Burgers方程,得到三角激波解;在不稳定区域,推导出mKdV方程,得到车头间距的扭结-反扭结波解;在亚稳定区域,推导出KdV方程,得到车头间距的孤立波解. 其次,假设司机对车头间距和速度差的反应时滞相同的条件下,我们引入了含两个同时滞的多速度差交通流模型.运用线性稳定性理论分析得到了范围更广的稳定性条件.利用约化摄动法导出了非线性密度波方程,进而利用这些方程的孤波解来描述此模型的非线性动力学特征. 最后,假设司机对车头间距和速度差的反应时滞不同的条件下,我们引入含两个时滞的多速度差交通流模型.利用约化摄动法导出了非线性密度波方程,进而利用这些方程的孤波解来描述此模型的非线性动力学特征.
[Abstract]:With the development of high and new technology, delay effect has become one of the key factors in the process of solving practical problems. In recent years, the influence of delay effect on traffic flow has been paid more and more attention by experts and scholars in various fields. In the traffic flow following model, the effect of driver response delay and mechanical delay on traffic flow can not be ignored. In this paper, the delay is introduced into the car-following model and the results are obtained by using the stability analysis and the reduced perturbation method. The main works are as follows: firstly, the linear stability analysis is used to obtain the stability condition by introducing the asymmetric full speed differential traffic flow model with time delay. The nonlinear dynamic characteristics of the model are analyzed by the reductive perturbation method: in the steady flow region, the Burgers equation is derived and the triangular shock wave solution is obtained; in the unstable region, the mKdV equation is derived and the kink and anti-kink wave solution of the headspace is obtained. In the metastable region, the KdV equation is derived and the solitary-wave solution of the headspace is obtained. Secondly, assuming that the drivers have the same time delay to the headway spacing and velocity difference, we introduce a multi-velocity differential traffic flow model with two simultaneous delays. The linear stability theory is applied to obtain a wider range of stability conditions. The nonlinear density wave equations are derived by using the reduced perturbation method, and the nonlinear dynamic characteristics of the model are described by using the solitary wave solutions of these equations. Finally, we introduce a multi-speed differential traffic flow model with two delays, assuming that the drivers react to the headway spacing and the velocity difference with different time delays. The nonlinear density wave equations are derived by using the reduced perturbation method, and the nonlinear dynamic characteristics of the model are described by using the solitary wave solutions of these equations.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U491.112
本文编号：2226079
[Abstract]:With the development of high and new technology, delay effect has become one of the key factors in the process of solving practical problems. In recent years, the influence of delay effect on traffic flow has been paid more and more attention by experts and scholars in various fields. In the traffic flow following model, the effect of driver response delay and mechanical delay on traffic flow can not be ignored. In this paper, the delay is introduced into the car-following model and the results are obtained by using the stability analysis and the reduced perturbation method. The main works are as follows: firstly, the linear stability analysis is used to obtain the stability condition by introducing the asymmetric full speed differential traffic flow model with time delay. The nonlinear dynamic characteristics of the model are analyzed by the reductive perturbation method: in the steady flow region, the Burgers equation is derived and the triangular shock wave solution is obtained; in the unstable region, the mKdV equation is derived and the kink and anti-kink wave solution of the headspace is obtained. In the metastable region, the KdV equation is derived and the solitary-wave solution of the headspace is obtained. Secondly, assuming that the drivers have the same time delay to the headway spacing and velocity difference, we introduce a multi-velocity differential traffic flow model with two simultaneous delays. The linear stability theory is applied to obtain a wider range of stability conditions. The nonlinear density wave equations are derived by using the reduced perturbation method, and the nonlinear dynamic characteristics of the model are described by using the solitary wave solutions of these equations. Finally, we introduce a multi-speed differential traffic flow model with two delays, assuming that the drivers react to the headway spacing and the velocity difference with different time delays. The nonlinear density wave equations are derived by using the reduced perturbation method, and the nonlinear dynamic characteristics of the model are described by using the solitary wave solutions of these equations.
【学位授予单位】：云南师范大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：U491.112
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