IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v16y2024i13p5721-d1428951.html
   My bibliography  Save this article

Analysis of Dynamic Behavior of Gravity Model Using the Techniques of Road Saturation and Hilbert Curve Dimensionality Reduction

Author

Listed:
  • Liumeng Yang

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

  • Ruichun He

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

  • Jie Wang

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

  • Hongxing Zhao

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

  • Huo Chai

    (School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China)

Abstract

In this study, we investigate the relationship between parameters and the dynamic behavior of traffic flow in road traffic systems, and we propose a segmented cost function to describe the effects of this flow on the dynamic gravity model at different saturation levels. We use single-parameter bifurcation analysis, maximum Lyapunov exponent calculation, and three-parameter bifurcation analysis to reveal the effects of parameter variations on the nonlinear dynamical behaviors of the modified gravity model, and we investigate the evolution laws of the traffic system in depth. In order to solve the problems of low efficiency and poor visualization ability in traditional dynamics analysis techniques, this paper proposes the Hilbert curve dimensionality reduction technique, which can completely retain the original data features. The three-dimensional pseudo-Hilbert curve is used to traverse the three-parameter bifurcation data, realizing the transformation of data from three- to one-dimensional. Then, the two-dimensional pseudo-Hilbert curve is used to traverse the reduced one-dimensional data, and the two-dimensional visualization of the three-parameter bifurcation diagram is successfully realized. The dimensionality reduction technique provides a new way of thinking for parameter analysis in the engineering field. By analyzing the two-dimensional bifurcation plan obtained after this reduction, it is found that the modified gravity model is more stable compared with the original model, and this conclusion is also verified by the wavelet transform results. Finally, a new robustness evaluation index is defined based on the dynamics of the model, and the simulation results reveal the intrinsic correlation between the saturation parameter and road congestion, which provides an important basis for promoting sustainable transportation in the road network.

Suggested Citation

  • Liumeng Yang & Ruichun He & Jie Wang & Hongxing Zhao & Huo Chai, 2024. "Analysis of Dynamic Behavior of Gravity Model Using the Techniques of Road Saturation and Hilbert Curve Dimensionality Reduction," Sustainability, MDPI, vol. 16(13), pages 1-19, July.
    • Handle: RePEc:gam:jsusta:v:16:y:2024:i:13:p:5721-:d:1428951
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/16/13/5721/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/16/13/5721/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sajan, & Kumar Choudhary, Kapil & Dubey, Balram, 2023. "A non-autonomous approach to study the impact of environmental toxins on nutrient-plankton system," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    2. Tian, Zhongda, 2020. "Chaotic characteristic analysis of network traffic time series at different time scales," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Hong, Inho & Jung, Woo-Sung, 2016. "Application of gravity model on the Korean urban bus network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 48-55.
    4. Faradja, Philippe & Qi, Guoyuan, 2020. "Analysis of multistability, hidden chaos and transient chaos in brushless DC motor," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    5. Edwidge Raissa Mache Kengne & Alain Soup Tewa Kammogne & Thomas Tatietse Tamo & Ahmad Taher Azar & Ahmed Redha Mahlous & Saim Ahmed, 2023. "Photovoltaic Systems Based on Average Current Mode Control: Dynamical Analysis and Chaos Suppression by Using a Non-Adaptive Feedback Outer Loop Controller," Sustainability, MDPI, vol. 15(10), pages 1-24, May.
    6. Filippo Simini & Marta C. González & Amos Maritan & Albert-László Barabási, 2012. "A universal model for mobility and migration patterns," Nature, Nature, vol. 484(7392), pages 96-100, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Yanguang, 2023. "Demonstration of duality of fractal gravity models by scaling symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Li, Xueyan & Qiu, Heting & Yang, Yanni & Zhang, Hankun, 2022. "Differentiated fares depend on bus line and time for urban public transport network based on travelers’ day-to-day group behavior," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    3. Méndez-Gordillo, Alma Rosa & Cadenas, Erasmo, 2021. "Wind speed forecasting by the extraction of the multifractal patterns of time series through the multiplicative cascade technique," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Zhang, Yuan & Cao, Jinde & Liu, Lixia & Liu, Haihong & Li, Zhouhong, 2024. "Complex role of time delay in dynamical coordination of neural progenitor fate decisions mediated by Notch pathway," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    5. Tranos, Emmanouil & Incera, Andre Carrascal & Willis, George, 2022. "Using the web to predict regional trade flows: data extraction, modelling, and validation," OSF Preprints 9bu5z, Center for Open Science.
    6. Huang, Feihu & Qiao, Shaojie & Peng, Jian & Guo, Bing & Xiong, Xi & Han, Nan, 2019. "A movement model for air passengers based on trip purpose," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 798-808.
    7. Varga, Levente & Tóth, Géza & Néda, Zoltán, 2017. "An improved radiation model and its applicability for understanding commuting patterns in Hungary," MPRA Paper 76806, University Library of Munich, Germany.
    8. Sgrignoli, Paolo & Metulini, Rodolfo & Schiavo, Stefano & Riccaboni, Massimo, 2015. "The relation between global migration and trade networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 245-260.
    9. James Truscott & Neil M Ferguson, 2012. "Evaluating the Adequacy of Gravity Models as a Description of Human Mobility for Epidemic Modelling," PLOS Computational Biology, Public Library of Science, vol. 8(10), pages 1-12, October.
    10. Chen, Yong & Geng, Maosi & Zeng, Jiaqi & Yang, Di & Zhang, Lei & Chen, Xiqun (Michael), 2023. "A novel ensemble model with conditional intervening opportunities for ride-hailing travel mobility estimation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 628(C).
    11. Chaogui Kang & Yu Liu & Diansheng Guo & Kun Qin, 2015. "A Generalized Radiation Model for Human Mobility: Spatial Scale, Searching Direction and Trip Constraint," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-11, November.
    12. Luo, Xiaohu & Caron, Justin & Karplus, Valerie J. & Zhang, Da & Zhang, Xiliang, 2016. "Interprovincial migration and the stringency of energy policy in China," Energy Economics, Elsevier, vol. 58(C), pages 164-173.
    13. Mark Thissen & Olga Ivanova & Giovanni Mandras & Trond Husby, 2019. "European NUTS 2 regions: construction of interregional trade-linked Supply and Use tables with consistent transport flows," JRC Working Papers on Territorial Modelling and Analysis 2019-01, Joint Research Centre.
    14. Thompson, C.A. & Saxberg, K. & Lega, J. & Tong, D. & Brown, H.E., 2019. "A cumulative gravity model for inter-urban spatial interaction at different scales," Journal of Transport Geography, Elsevier, vol. 79(C), pages 1-1.
    15. Gonzalo Suarez & Rachata Muneepeerakul, 2022. "Modeling human migration driven by changing mindset, agglomeration, social ties, and the environment," PLOS ONE, Public Library of Science, vol. 17(2), pages 1-11, February.
    16. Rosita De Vincentis & Federico Karagulian & Carlo Liberto & Marialisa Nigro & Vincenza Rosati & Gaetano Valenti, 2022. "A Data-Driven Approach to Analyze Mobility Patterns and the Built Environment: Evidence from Brescia, Catania, and Salerno (Italy)," Sustainability, MDPI, vol. 14(21), pages 1-14, November.
    17. Vinyas Harish & Felipe J. Colón-González & Filipe R. R. Moreira & Rory Gibb & Moritz U. G. Kraemer & Megan Davis & Robert C. Reiner & David M. Pigott & T. Alex Perkins & Daniel J. Weiss & Isaac I. Bog, 2024. "Human movement and environmental barriers shape the emergence of dengue," Nature Communications, Nature, vol. 15(1), pages 1-15, December.
    18. Animesh Gain & Vahid Mojtahed & Claudio Biscaro & Stefano Balbi & Carlo Giupponi, 2015. "An integrated approach of flood risk assessment in the eastern part of Dhaka City," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 79(3), pages 1499-1530, December.
    19. Wang, Wenjun & Pan, Lin & Yuan, Ning & Zhang, Sen & Liu, Dong, 2015. "A comparative analysis of intra-city human mobility by taxi," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 134-147.
    20. S. Bacci & B. Bertaccini, 2021. "Assessment of the University Reputation Through the Analysis of the Student Mobility," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 156(2), pages 363-388, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jsusta:v:16:y:2024:i:13:p:5721-:d:1428951. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.