Bifurcation analysis and control of the full velocity difference model with delayed velocity difference

IF 1.8 4区物理与天体物理 Q4 CHEMISTRY, PHYSICAL

The European Physical Journal E Pub Date : 2024-12-08 DOI:10.1140/epje/s10189-024-00462-3

Wenhuan Ai, Guoao Li, Jianhua Zhang, Xiaoshuang Zhu, Dawei Liu

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引用次数: 0

Abstract

With the increase in the number of urban vehicles, various traffic problems have gradually emerged. Studying the causes of traffic congestion and proposing effective mitigation strategies have important practical significance. This paper proposes a macroscopic traffic flow model that considers the delayed speed difference. This paper applies nonlinear bifurcation to describe and predict nonlinear traffic phenomena on highways from the perspective of global stability of the traffic system. By using the traveling wave transformation, the proposed car-following model is converted into a macroscopic traffic flow model. Next, this paper employs the linear stability analysis to find the bifurcation points of the stability transition in the traffic system, exploring the qualitative characteristics of the inhomogeneous continuous traffic flow model. Theoretical derivations demonstrate the existence of bifurcation points within the model. Additionally, this paper plots the density-time space diagrams and phase plane diagrams of the system to visually present the sudden changes in traffic flow as variable parameters pass through these bifurcation points. Finally, this paper designs a feedback controller to regulate the Hopf bifurcation, aiming to delay or eliminate the occurrence of Hopf bifurcations in the stochastic system.

Graphical abstract

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时滞速度差全速度差模型的分岔分析与控制

随着城市车辆数量的增加，各种交通问题逐渐显现。研究交通拥堵的成因并提出有效的缓解策略具有重要的现实意义。本文提出了一个考虑延迟速度差的宏观交通流模型。本文从交通系统全局稳定性的角度出发，运用非线性分岔理论来描述和预测公路上的非线性交通现象。通过行波变换，将所提出的车辆跟随模型转化为宏观交通流模型。其次，本文采用线性稳定性分析方法寻找交通系统稳定性过渡的分岔点，探讨非齐次连续交通流模型的定性特征。理论推导证明了模型中存在分岔点。并绘制了系统的密度-时间-空间图和相平面图，直观地呈现了变参数经过这些分岔点时交通流的突变。最后，本文设计了一个反馈控制器来调节Hopf分岔，目的是延迟或消除随机系统中Hopf分岔的发生。图形抽象

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

The European Physical Journal E CHEMISTRY, PHYSICAL-MATERIALS SCIENCE, MULTIDISCIPLINARY

CiteScore

2.60

自引率

5.60%

发文量

审稿时长

3 months

期刊介绍： EPJ E publishes papers describing advances in the understanding of physical aspects of Soft, Liquid and Living Systems. Soft matter is a generic term for a large group of condensed, often heterogeneous systems -- often also called complex fluids -- that display a large response to weak external perturbations and that possess properties governed by slow internal dynamics. Flowing matter refers to all systems that can actually flow, from simple to multiphase liquids, from foams to granular matter. Living matter concerns the new physics that emerges from novel insights into the properties and behaviours of living systems. Furthermore, it aims at developing new concepts and quantitative approaches for the study of biological phenomena. Approaches from soft matter physics and statistical physics play a key role in this research. The journal includes reports of experimental, computational and theoretical studies and appeals to the broad interdisciplinary communities including physics, chemistry, biology, mathematics and materials science.