基于跟驰模型的交通流分岔与混沌研究
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摘要
本文的目标是分析车辆跟驰模型中的非线性动力学行为,以寻求交通流中各种非线性现象产生的基本机理。
从有序到无序、再从无序到有序,是交通流中普遍存在的一种形式。交通流在一定条件下有可能在状态转化过程中出现混沌现象,这一事实已经被一些学者研究并从多角度所证实。本文在认真分析国内外交通流该领域研究现状的基础上,综合评述己有的成果,发现已有的研究缺乏对交通流混沌产生机理的分析,因此选择将分岔理论引入交通流混沌的研究作为突破方向,通过对交通流中由于稳定性丧失而导致的分岔现象进行研究,进一步分析了由分岔演化至混沌的不同途径,说明了交通流混沌产生的复杂性。
文章的主要内容如下:
利用非线性系统的稳定性理论分析了刺激-反应模型模型和优化速度模型的系统稳定性条件,简要介绍了三相交通流理论,并结合稳定性条件,通过对不同交通流状态之间转化的模拟仿真,发现了同一交通相下交通流状态的多样性特征,同时对相变过程中的连续相变与不连续相变进行了讨论。
分别研究了无时滞参数和带时滞参数的交通流优化速度模型中的分岔现象,利用非线性系统的稳定性分析理论,给出了Hopf分岔产生时,各参数满足的临界关系表达式,并在时滞微分方程理论的基础上,通过中心流形方法和正规型的计算,推导出了确定Hopf分岔方向和分岔解稳定性的判别式,同时利用仿真软件分析了分岔行为对交通流状态的影响,并讨论了分岔行为的进一步演化至混沌的可能性。
从分析车辆跟驰行为中的基本混沌特征入手,结合定量和定性的方法,在以往混沌识别算法的基础上,提出了基于组合特征分析的算法来验证交通流中的混沌现象存在性问题,并据此对速度优化模型的混沌现象进行了研究,同时讨论了模型中参数对交通流状态的影响。
在对交通流模型中混沌分析的基础上,结合分岔理论,通过形式推演、计算机模拟等方法对交通流模型中的混沌产生的基本途径分别进行了分析,发现在一定参数条件下,交通流系统中确实会出现混沌现象,并且混沌是通过分岔行为的演化,沿袭倍周期分岔、阵发性以及Hopf分岔等不同的途径而引发的。
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
从有序到无序、再从无序到有序,是交通流中普遍存在的一种形式。交通流在一定条件下有可能在状态转化过程中出现混沌现象,这一事实已经被一些学者研究并从多角度所证实。本文在认真分析国内外交通流该领域研究现状的基础上,综合评述己有的成果,发现已有的研究缺乏对交通流混沌产生机理的分析,因此选择将分岔理论引入交通流混沌的研究作为突破方向,通过对交通流中由于稳定性丧失而导致的分岔现象进行研究,进一步分析了由分岔演化至混沌的不同途径,说明了交通流混沌产生的复杂性。
文章的主要内容如下:
利用非线性系统的稳定性理论分析了刺激-反应模型模型和优化速度模型的系统稳定性条件,简要介绍了三相交通流理论,并结合稳定性条件,通过对不同交通流状态之间转化的模拟仿真,发现了同一交通相下交通流状态的多样性特征,同时对相变过程中的连续相变与不连续相变进行了讨论。
分别研究了无时滞参数和带时滞参数的交通流优化速度模型中的分岔现象,利用非线性系统的稳定性分析理论,给出了Hopf分岔产生时,各参数满足的临界关系表达式,并在时滞微分方程理论的基础上,通过中心流形方法和正规型的计算,推导出了确定Hopf分岔方向和分岔解稳定性的判别式,同时利用仿真软件分析了分岔行为对交通流状态的影响,并讨论了分岔行为的进一步演化至混沌的可能性。
从分析车辆跟驰行为中的基本混沌特征入手,结合定量和定性的方法,在以往混沌识别算法的基础上,提出了基于组合特征分析的算法来验证交通流中的混沌现象存在性问题,并据此对速度优化模型的混沌现象进行了研究,同时讨论了模型中参数对交通流状态的影响。
在对交通流模型中混沌分析的基础上,结合分岔理论,通过形式推演、计算机模拟等方法对交通流模型中的混沌产生的基本途径分别进行了分析,发现在一定参数条件下,交通流系统中确实会出现混沌现象,并且混沌是通过分岔行为的演化,沿袭倍周期分岔、阵发性以及Hopf分岔等不同的途径而引发的。
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
引文
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