【摘要】：隨著各種高新技術(shù)的發(fā)展,時(shí)滯效應(yīng)在解決實(shí)際問題的過程中成為關(guān)鍵因素之一.近年來,時(shí)滯效應(yīng)對(duì)交通流的影響受到各相關(guān)領(lǐng)域?qū)＜覍W(xué)者的廣泛關(guān)注.在交通流跟馳模型中,由于司機(jī)反應(yīng)時(shí)滯以及機(jī)械時(shí)滯,對(duì)交通流的影響是不可忽略的. 本文將時(shí)滯引入到跟馳模型中,運(yùn)用穩(wěn)定性分析和約化攝動(dòng)法分析獲得了比較理想的結(jié)果.具體工作如下: 首先,引入含時(shí)滯不對(duì)稱全速度差交通流模型,運(yùn)用線性穩(wěn)定性分析得到穩(wěn)定性條件,通過約化攝動(dòng)法分析此模型的非線性動(dòng)力學(xué)特征:在穩(wěn)定流區(qū)域,推導(dǎo)出Burgers方程,得到三角激波解;在不穩(wěn)定區(qū)域,推導(dǎo)出mKdV方程,得到車頭間距的扭結(jié)-反扭結(jié)波解;在亞穩(wěn)定區(qū)域,推導(dǎo)出KdV方程,得到車頭間距的孤立波解. 其次,假設(shè)司機(jī)對(duì)車頭間距和速度差的反應(yīng)時(shí)滯相同的條件下,我們引入了含兩個(gè)同時(shí)滯的多速度差交通流模型.運(yùn)用線性穩(wěn)定性理論分析得到了范圍更廣的穩(wěn)定性條件.利用約化攝動(dòng)法導(dǎo)出了非線性密度波方程,進(jìn)而利用這些方程的孤波解來描述此模型的非線性動(dòng)力學(xué)特征. 最后,假設(shè)司機(jī)對(duì)車頭間距和速度差的反應(yīng)時(shí)滯不同的條件下,我們引入含兩個(gè)時(shí)滯的多速度差交通流模型.利用約化攝動(dòng)法導(dǎo)出了非線性密度波方程,進(jìn)而利用這些方程的孤波解來描述此模型的非線性動(dòng)力學(xué)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.
【學(xué)位授予單位】：云南師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：U491.112

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本文編號(hào)：2226079