Wave dynamics in an extended macroscopic traffic flow model with periodic boundaries

Wang, Yuqing; Chu, Xing-Jian; Zhou, Cancan; Yan, Bowen; Jia, Bin; Fang, Chenhao

doi:10.1142/s0217984918501683

Cited by 16 publications

(3 citation statements)

References 51 publications

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“…The mathematical model describing the actual traffic law is the main tool to reveal the basic law of traffic flow. Researchers have now proposed a large number of traffic flow models, mainly including three types: cellular automata model [1][2][3] , micro car-following model [4][5][6][7][8] , and macro dynamics model [9][10][11][12][13] . However, due to the complexity of the traffic system, various traffic phenomena in actual traffic such as vehicles Stopping at all times, increased vehicle density, increased vehicle speed, etc.…”

Section: Introductionmentioning

confidence: 99%

Branch Analysis of Macro-Traffic Flow Model With Different Driving Characteristics in Its Environment

Ai¹,

Xing

et al. 2021

IEEE Access

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Research of traffic phenomena is the application basis of intelligent transportation systems and plays an important role in enriching the theoretical system of modern traffic flow. Various nonlinear traffic phenomena in the transportation system often alternately change, and the essence of these changes is theoretically a branching behavior. When the traffic system parameters change to a critical value, the qualitative state of the traffic flow, such as the free-running state, the blocking state, and the stop-and-go state, will undergo abrupt changes. However, previous studies on the bifurcation phenomenon of traffic flow mainly focused on the microscopic car-following model from the perspective of local stability, and the bifurcation analysis of the macroscopic traffic flow model has not been reported. Therefore, this article applies branch theory to study the classic macroscopic traffic flow model. First, the types of equilibrium points and their stable states of the model equations are studied, and the global distribution structure of the equilibrium points in the phase plane is drawn to verify the consistency of the numerical and analytical solutions. Secondly, the theory deduces the existence conditions of the model, and simulations have obtained various systems such as Hopf bifurcation, saddle knot bifurcation, limit cycle bifurcation, cusp bifurcation (CP), Bogdanov-Takens (BT) bifurcation, and so on. Finally, starting from the Hopf branch and the saddle-node branch point, by drawing the density space-time diagram of the system, the stop-and-go phenomenon and local aggregation phenomenon in actual traffic are better explained. The results obtained in this paper show that the branch analysis method can better describe the nonlinear traffic phenomena on urban roads, and can provide a theoretical basis for the implementation of traffic control strategies. At the same time, it also has a very broad application prospect for the development of traffic control software in intelligent transportation systems.

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Section: Introductionmentioning

confidence: 99%

Branch Analysis of Macro-Traffic Flow Model With Different Driving Characteristics in Its Environment

Ai¹,

Xing

et al. 2021

IEEE Access

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“…[1][2][3][4] In general, the complex network can be divided into small world networks, [5] self-similarity ones, [6] regular ones, [7] partly or wholly heterogeneous one. [8] It is capable of modelling real physical or engineering phenomena like traffic flow, [9][10][11][12][13][14][15] the transcription of mRNA, [16] the directional motion of active particles, [17][18][19][20][21][22][23][24][25] etc., which leads the technology networks, [26] social networks, [27] financial network, [28][29][30][31][32][33][34][35][36][37][38][39] biological networks, etc. to emerge.…”

Section: Introductionmentioning

confidence: 99%

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms*

Shi-Zhao

Wang

2019

Chinese Phys. B

Self Cite

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In the field of statistical mechanics and system science, it is acknowledged that the financial crisis has a profound influence on stock market. However, the influence of total asset of enterprise on stock quote was not considered in the previous studies. In this work, a modified cross-correlation matrix that focuses on the influence of total asset on stock quote is introduced into the analysis of the stocks collected from Asian and American stock markets, which is different from the previous studies. The key results are obtained as follows. Firstly, stock is more greatly correlated with big asset than with small asset. Secondly, the higher the correlation coefficient among stocks, the larger the eigenvector is. Thirdly, in different periods, like the pre-subprime crisis period and the peak of subprime crisis period, Asian stock quotes show that the component of the third eigenvector of the cross-correlation matrix decreases with the asset of the enterprise decreasing. Fourthly, by simulating the threshold network, the small network constructed by 10 stocks with large assets can show the large network state constructed by 30 stocks. In this research we intend to fully explain the physical mechanism for understanding the historical correlation between stocks and provide risk control strategies in the future.

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“…In order to replicate the evolution of traffic, there is the need for a mathematical modeling of the traffic flow [13][14][15][16][17][18][19][20]. In this regard, scholars have examined a (a) E-mail: poonamr.maths@mdurohtak.ac.in (corresponding author) variety of car-following models [21][22][23][24][25][26] recently, and these models are used to examine the effects of various factors on the traffic flow.…”

mentioning

confidence: 99%

Impact of driver's advanced reaction time in car-following model with optimal velocity deviation under V2X environment

Yadav,

Siwach,

Redhu

2023

EPL

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The vehicle-to-everything (V2X) technology has made a significant advancement in the field of intelligent transportation in recent years. When operating a vehicle in a V2X environment, the driver can get real-time updates on the motion of nearby vehicles. In a real-world traffic situation, there is always some deviation between the actual and anticipated traffic information, and this deviation will undoubtedly have a significant effect on traffic flow. Drivers always maintain the flow of traffic by taking some time to assess and decide how the drivers in front of them are behaving behind the car in the traffic system. As a result, by taking into account the driver's advanced reaction time and optimal deviation in a V2X environment, a novel car-following model is developed and the effects of these parameters on the traffic flow are examined. In order to determine the stability requirements for the new model, the linear and nonlinear stability of the proposed model is examined using the perturbation methods. Studies have found that when the driver's reaction time and the velocity deviation are optimized, it can reduce the amplitude of the stability curve, thus enlarging the area of more stable motion. Also, the numerical simulation supports the theoretical research by showing that the new model may effectively reduce traffic congestion and improve the stability of traffic flow as the influence of these factors on the traffic flow increases.

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Wave dynamics in an extended macroscopic traffic flow model with periodic boundaries

Cited by 16 publications

References 51 publications

Branch Analysis of Macro-Traffic Flow Model With Different Driving Characteristics in Its Environment

Branch Analysis of Macro-Traffic Flow Model With Different Driving Characteristics in Its Environment

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms*

Impact of driver's advanced reaction time in car-following model with optimal velocity deviation under V2X environment

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