守恒高阶交通流模型的相平面分析

吴春秀; 宋涛; 张鹏; 黄仕进

doi:10.3879/j.issn.1000-0887.2012.12.003

守恒高阶交通流模型的相平面分析

doi: 10.3879/j.issn.1000-0887.2012.12.003

吴春秀^1,2,
宋涛^1,2,
张鹏^1,2,
黄仕进³

¹上海大学,上海市应用数学和力学研究所,上海 200072;²上海市力学在工程中的应用重点实验室,上海 200072;
香港大学土木工程系,香港

基金项目: 国家自然科学基金资助项目(11072141)；上海高校创新团队建设项目

详细信息

作者简介:
吴春秀 (1978—),女,安徽人,博士研究生(E-mail: wuchunxiu@shu.edu.cn);张鹏,教授(联系人.E-mail: pzhang@mail.shu.edu.cn).

中图分类号: O29; U121
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- 被引次数: 0
出版历程
- 收稿日期: 2012-01-05
- 修回日期: 2012-04-30
- 刊出日期: 2012-12-15

Phase-plane analysis of conserved higher-order traffic flow model

¹ Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;²Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China;³Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China

Funds: Project supported by the National Natural Science Foundation of China (No. 11072141), the Shanghai Program for Innovative Research Team in Universities, the Graduate Innovation Foundation of Shanghai University (No. SHUCX101078), and the University Research Committee, HKU SPACE Research Fund and Faculty of Engineering Top-up Grant of the University of Hong Kong (No. 201007176059)

摘要

摘要: 在Lagrange坐标下，运用微分方程定性理论中的相平面分析方法，研究一个近期所提出的守恒高阶交通流模型的行波解．讨论系统的平衡点类型及其稳定性状态，分析相平面中的轨线全局分布结构，验证数值解与解析解的一致性．从而，能够较好地解释现实交通中的时停时走波和瓶颈处的振荡现象，表明所讨论的模型能够描述复杂的拥挤交通．
- 交通流 /
- Lagrange坐标 /
- 相平面分析 /
- 拥挤交通模式
Abstract: The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.
- traffic flow /
- Lagrange coordinates /
- phase-plane analysis /
- traffic congestion pattern

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参考文献(20)

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