二维交通网络动力学中的临界点、多稳定性和随机性。

IF 3.2 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-07-01 DOI:10.1063/5.0202785
Shankha Narayan Chattopadhyay, Arvind Kumar Gupta
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引用次数: 0

摘要

城市交通系统由大量相互连接的路线组成一个错综复杂的网络,缓解交通拥堵是改善城市交通系统的关键步骤。为了解网络上车辆交通流的显著特点,我们提出了一个宏观的二维交通网络模型,其中包含节点内和节点间的车辆相互作用。利用流行的非线性动力学技术,我们研究了不同参数的影响,如车辆的占用率、进入率和退出率。使用单参数或双参数分岔图显示了鞍节点、霍普夫、同线性、波格丹诺夫-塔肯斯和尖顶分岔的存在。我们还详细探讨了不同多稳态(双稳态/三稳态)现象、随机切换和临界转换的发生。此外,我们还利用盆地稳定性度量计算了实现每种替代状态的可能性,以表征多稳定性。此外,我们还确定了不同随机波动幅度下从自由流动到拥堵的临界转换。研究了基于临界减速通用指标(如方差、滞后-1 自相关性、偏斜度、峰度和条件异方差)的适用性,以预示从自由流动到交通拥堵的临界过渡。通过使用模拟数据证明,并非所有指标都对交通流量的快速阶段转换表现出敏感性。我们的研究表明,交通拥堵的出现是由于分岔或随机性造成的。本研究提供的结果可作为理解交通堵塞定性行为的范例,并可用于探索交通现象中出现的临界机制。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Tipping points, multistability, and stochasticity in a two-dimensional traffic network dynamics.

Mitigating traffic jams is a critical step for the betterment of the urban transportation system, which comprises a large number of interconnected routes to form an intricate network. To understand distinct features of vehicular traffic flow on a network, a macroscopic two-dimensional traffic network model is proposed incorporating intra-nodal and inter-nodal vehicular interaction. Utilizing the popular techniques of nonlinear dynamics, we investigate the impact of different parameters like occupancy, entry rates, and exit rates of vehicles. The existence of saddle-node, Hopf, homoclinic, Bogdanov-Takens, and cusp bifurcations have been shown using single or biparametric bifurcation diagrams. The occurrences of different multistability (bistability/tristability) phenomena, stochastic switching, and critical transitions are explored in detail. Further, we calculate the possibility of achieving each alternative state using the basin stability metric to characterize multistability. In addition, critical transitions from free flow to congestion are identified at different magnitudes of stochastic fluctuations. The applicability of critical slowing down based generic indicators, e.g., variance, lag-1 autocorrelation, skewness, kurtosis, and conditional heteroskedasticity are investigated to forewarn the critical transition from free flow to traffic congestion. It is demonstrated through the use of simulated data that not all of the measures exhibit sensitivity to rapid phase transitions in traffic flow. Our study reveals that traffic congestion emerges because of either bifurcation or stochasticity. The result provided in this study may serve as a paradigm to understand the qualitative behavior of traffic jams and to explore the tipping mechanisms occurring in transport phenomena.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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