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Spontaneous synchronization of motion in pedestrian crowds of different densities

Abstract

Interacting pedestrians in a crowd spontaneously adjust their footsteps and align their respective stepping phases. This self-organization phenomenon is known as synchronization. However, it is unclear why and how synchronization forms spontaneously under different density conditions, or what functional benefit synchronization offers for the collective motion of humans. Here, we conducted a single-file crowd motion experiment that directly tracked the alternating movement of both legs of interacting pedestrians. We show that synchronization is most likely to be triggered at the same density at which the flow rate of pedestrians reaches a maximum value. We demonstrate that synchronization is established in response to an insufficient safety distance between pedestrians, and that it enables pedestrians to realize efficient collective stepping motion without the occurrence of inter-person collisions. These findings provide insights into the collective motion behaviour of humans and may have implications for understanding pedestrian synchronization-induced wobbling, for example, of bridges.

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Fig. 1: Experimental design.
Fig. 2: Schematic of the method used to extract footstep samples.
Fig. 3: Schematic of the synchronization between the following pedestrian i and the predecessor pedestrian in the exemplary time–space (that is, foot position versus time) diagram of the foot motions.
Fig. 4: Statistical results of the local densities over all 552 detected pairs of synchronized successive pedestrians.
Fig. 5: Velocity and flow characteristics at different densities.
Fig. 6: Empirical evidence that synchronization is most likely to be induced when the flow rate of pedestrians reaches its maximum value.
Fig. 7: Interpretation of the formation mechanism of synchronization.

Data availability

The data necessary to support the findings of this manuscript are available in a public repository (https://zenodo.org/record/3732248).

Code availability

The custom code used is available in an online repository (https://github.com/mayifromcqhc/Crowd-synchronization).

References

  1. 1.

    Helbing, D., Farkas, I. J. & Vicsek, T. Simulating dynamical features of escape panic. Nature 407, 487–490 (2000).

    CAS  PubMed  Google Scholar 

  2. 2.

    Low, D. J. Statistical physics: following the crowd. Nature 407, 465–466 (2000).

    CAS  PubMed  Google Scholar 

  3. 3.

    Helbing, D. & Johansson, A. in Encyclopedia of Complexity and Systems Science (ed. Meyers, R. A.) 6476–6495 (Springer, 2009).

  4. 4.

    Schadschneider, A. et al. in Encyclopedia of Complexity and Systems Science (ed. Meyers, R. A.) 3142–3176 (Springer, 2009).

  5. 5.

    Timmermans, H. Pedestrian Behavior: Models, Data Collection and Applications (Emerald Group Publishing, 2009).

  6. 6.

    Helbing, D., Buzna, L. & Werner, J. T. Self-organized pedestrian crowd dynamics: experiments, simulations, and design solutions. Transport Sci. 39, 1–24 (2005).

    Google Scholar 

  7. 7.

    Johansson, A. Constant-net-time headway as a key mechanism behind pedestrian flow dynamics. Phys. Rev. E 80, 026120 (2009).

    Google Scholar 

  8. 8.

    Kuang, H., Li, X., Song, T. & Dai, S. Analysis of pedestrian dynamics in counter flow via an extended lattice gas model. Phys. Rev. E 78, 066117 (2008).

    Google Scholar 

  9. 9.

    Hoogendoorn, S. P. & Daamen, W. Pedestrian behavior at bottlenecks. Transp. Sci. 39, 147–159 (2005).

    Google Scholar 

  10. 10.

    Moussaid, M. et al. Traffic instabilities in self-organized pedestrian crowds. PLoS Comput. Biol. 8, e1002442 (2012).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Moussaid, M. et al. Experimental study of the behavioural mechanisms underlying self-organization in human crowds. Proc. R. Soc. B 276, 2755–2762 (2009).

    PubMed  Google Scholar 

  12. 12.

    Zhang, J. et al. Universal flow-density relation of single-file bicycle, pedestrian and car motion. Phys. Lett. A 378, 3274–3277 (2014).

    CAS  Google Scholar 

  13. 13.

    Corbetta, A., Meeusen, J. A., Lee, C. M., Benzi, R. & Toschi, F. Physics-based modeling and data representation of pairwise interactions among pedestrians. Phys. Rev. E 98, 062310 (2018).

    CAS  Google Scholar 

  14. 14.

    Rio, K., Bonneaud, S. & Warren, W. H. Speed coordination in pedestrian groups: linking individual locomotion with crowd behavior. J. Vis. 12, 190 (2012).

    Google Scholar 

  15. 15.

    Rio, K. W. & Warren, W. H. A speed control law for pedestrian following based on visual angle. J. Vis. 11, 899 (2011).

    Google Scholar 

  16. 16.

    Page, Z. & Warren, W. H. Visual control of speed in side-by-side walking. J. Vis. 12, 188 (2012).

    Google Scholar 

  17. 17.

    Meerhoff, L. A., De Poel, H. J. & Button, C. How visual information influences coordination dynamics when following the leader. Neurosci. Lett. 582, 12–15 (2014).

    CAS  PubMed  Google Scholar 

  18. 18.

    Seyfried, A., Steffen, B., Klingsch, W. & Boltes, M.The fundamental diagram of pedestrian movement revisited. J. Stat. Mech. Theory Exp. 2005, P10002 (2005).

    Google Scholar 

  19. 19.

    Dallard, P. et al. London Millennium Bridge: pedestrian-induced lateral vibration. J. Bridge Eng. 6, 412–417 (2001).

    Google Scholar 

  20. 20.

    Strogatz, S. H., Abrams, D. M., McRobie, A., Eckhardt, B. & Ott, E. Theoretical mechanics: crowd synchrony on the Millennium Bridge. Nature 438, 43–44 (2005).

    CAS  PubMed  Google Scholar 

  21. 21.

    Eckhardt, B., Ott, E., Strogatz, S. H., Abrams, D. M. & McRobie, A. Modeling walker synchronization on the millennium bridge. Phys. Rev. E 75, 021110 (2007).

    Google Scholar 

  22. 22.

    Abdulrehem, M. M. & Ott, E. Low dimensional description of pedestrian-induced oscillation of the millennium bridge. Chaos 19, 013129 (2009).

    PubMed  Google Scholar 

  23. 23.

    Belykh, I., Jeter, R. & Belykh, V. Foot force models of crowd dynamics on a wobbly bridge. Sci. Adv. 3, e1701512 (2017).

    PubMed  PubMed Central  Google Scholar 

  24. 24.

    Patel, A. D., Iversen, J. R., Bregman, M. R. & Schulz, I. Experimental evidence for synchronization to a musical beat in a nonhuman animal. Curr. Biol. 19, 827–830 (2009).

    CAS  PubMed  Google Scholar 

  25. 25.

    Bode, N. W., Faria, J. J., Franks, D. W., Krause, J. & Wood, A. J. How perceived threat increases synchronization in collectively moving animal groups. Proc. R. Soc. B 277, 3065–3070 (2010).

    PubMed  Google Scholar 

  26. 26.

    Couzin, I. D. Synchronization: the key to effective communication in animal collectives. Trends Cogn. Sci. 22, 844–846 (2018).

    PubMed  Google Scholar 

  27. 27.

    Ashraf, I., Godoy-Diana, R., Halloy, J., Collignon, B. & Thiria, B. Synchronization and collective swimming patterns in fish (Hemigrammus bleheri). J. R. Soc. Interface 13, 20160734 (2016).

    PubMed  PubMed Central  Google Scholar 

  28. 28.

    Gao, J., Havlin, S., Xu, X. & Stanley, H. E. Angle restriction enhances synchronization of self-propelled objects. Phys. Rev. E 84, 046115 (2011).

    Google Scholar 

  29. 29.

    Liu, Z. & Guo, L. Synchronization of multi-agent systems without connectivity assumptions. Automatica 45, 2744–2753 (2009).

    Google Scholar 

  30. 30.

    Wang, L. & Chen, G. Synchronization of multi-agent systems with metric–topological interactions. Chaos 26, 094809 (2016).

    PubMed  Google Scholar 

  31. 31.

    Chattaraj, U., Seyfried, A. & Chakroborty, P. Comparison of pedestrian fundamental diagram across cultures. Adv. Complex Syst. 12, 393–405 (2009).

    Google Scholar 

  32. 32.

    Jelić, A., Appert-Rolland, C., Lemercier, S. & Pettré, J. Properties of pedestrians walking in line: fundamental diagrams. Phys. Rev. E 85, 036111 (2012).

    Google Scholar 

  33. 33.

    Jelić, A., Appert-Rolland, C., Lemercier, S. & Pettré, J. Properties of pedestrians walking in line. II. Stepping behavior. Phys. Rev. E 86, 046111 (2012).

    Google Scholar 

  34. 34.

    Fang, Z. M. et al. A continuous distance model (CDM) for the single-file pedestrian movement considering step frequency and length. Phys. A 391, 307–316 (2012).

    Google Scholar 

  35. 35.

    Cao, S. et al. Pedestrian dynamics in single-file movement of crowd with different age compositions. Phys. Rev. E 94, 012312 (2016).

    PubMed  Google Scholar 

  36. 36.

    Cao, S., Zhang, J., Song, W., Shi, C. A. & Zhang, R.The stepping behavior analysis of pedestrians from different age groups via a single-file experiment. J. Stat. Mech. Theory Exp. 2018, 033402 (2018).

    Google Scholar 

  37. 37.

    Zeng, G. et al. Experimental study on the effect of background music on pedestrian movement at high density. Phys. Lett. A 383, 1011–1018 (2019).

    CAS  Google Scholar 

  38. 38.

    Zeng, G., Cao, S., Liu, C. & Song, W. Experimental and modeling study on relation of pedestrian step length and frequency under different headways. Phys. A 500, 237–248 (2018).

    Google Scholar 

  39. 39.

    Wang, J. et al. Step styles of pedestrians at different densities. J. Stat. Mech. Theory Exp. 2018, 023406 (2018).

    Google Scholar 

  40. 40.

    Wang, J. et al. Linking pedestrian flow characteristics with stepping locomotion. Phys. A 500, 106–120 (2018).

    Google Scholar 

  41. 41.

    Yanagisawa, D., Tomoeda, A. & Nishinari, K. Improvement of pedestrian flow by slow rhythm. Phys. Rev. E 85, 016111 (2012).

    Google Scholar 

  42. 42.

    Ma, Y., Sun, Y. Y., Lee, E. W. M. & Yuen, R. K. K. Pedestrian stepping dynamics in single-file movement. Phys. Rev. E 98, 062311 (2018).

    CAS  Google Scholar 

  43. 43.

    Zhao, Y. & Zhang, H. M. A unified follow-the-leader model for vehicle, bicycle and pedestrian traffic. Transp. Res. B 105, 315–327 (2017).

    Google Scholar 

  44. 44.

    Seitz, M. J. & Köster, G. Natural discretization of pedestrian movement in continuous space. Phys. Rev. E 86, 046108 (2012).

    Google Scholar 

  45. 45.

    Seitz, M. J., Dietrich, F. & Köster, G. The effect of stepping on pedestrian trajectories. Phys. A 421, 594–604 (2015).

    Google Scholar 

  46. 46.

    Pimentel, R. L., Araújo, M. C. Jr, Braga Fernandes Brito, H. M. & Vital de Brito, J. L. Synchronization among pedestrians in footbridges due to crowd density. J. Bridge Eng. 18, 400–408 (2013).

    Google Scholar 

  47. 47.

    Gazzola, F. & Racic, V. A model of synchronisation in crowd dynamics. Appl. Math. Model. 59, 305–318 (2018).

    Google Scholar 

  48. 48.

    Joshi, V. & Srinivasan, M. Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony. Biol. Lett. 14, 20180564 (2018).

    PubMed  PubMed Central  Google Scholar 

  49. 49.

    Chambers, C., Kong, G., Wei, K. & Kording, K. Pose estimates from online videos show that side-by-side walkers synchronize movement under naturalistic conditions. PLoS ONE 14, e0217861 (2019).

    CAS  PubMed  PubMed Central  Google Scholar 

  50. 50.

    Ren, X., Zhang, J. & Song, W.Contrastive study on the single-file pedestrian movement of the elderly and other age groups. J. Stat. Mech. Theory Exp. 2019, 093402 (2019).

    Google Scholar 

  51. 51.

    Eilhardt, C. & Schadschneider, A. Stochastic headway dependent velocity model for 1D pedestrian dynamics at high densities. Transp. Res. Proc. 2, 400–405 (2014).

    Google Scholar 

  52. 52.

    Ziemer, V., Seyfried, A. & Schadschneider, A. in Traffic and Granular Flow ‘15 (eds. Knoop, V. L., & Daamen, W.) 89–96 (Springer, 2016).

  53. 53.

    Zhang, J., Klingsch, W., Schadschneider, A. & Seyfried, A.Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram. J. Stat. Mech. Theory Exp. 2012, P02002 (2012).

    Google Scholar 

  54. 54.

    Zhang, J., Klingsch, W., Schadschneider, A. & Seyfried, A.Transitions in pedestrian fundamental diagrams of straight corridors and T-junctions. J. Stat. Mech. Theory Exp. 2011, P06004 (2011).

    Google Scholar 

  55. 55.

    Vanumu, L. D., Rao, K. R. & Tiwari, G. Fundamental diagrams of pedestrian flow characteristics: a review. Eur. Transp. Res. Rev. 9, 49 (2017).

    Google Scholar 

  56. 56.

    Liu, X., Song, W. & Zhang, J. Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing. Phys. A 388, 2717–2726 (2009).

    CAS  Google Scholar 

  57. 57.

    Ma, J., Song, W. G., Fang, Z. M., Lo, S. M. & Liao, G. X. Experimental study on microscopic moving characteristics of pedestrians in built corridor based on digital image processing. Build. Environ. 45, 2160–2169 (2010).

    Google Scholar 

  58. 58.

    Chattaraj, U., Seyfried, A., Chakroborty, P. & Biswal, M. K. Modelling single file pedestrian motion across cultures. Proc. Soc. Behav. Sci. 104, 698–707 (2013).

    Google Scholar 

  59. 59.

    Helbing, D., Johansson, A. & Al-Abideen, H. Z. Dynamics of crowd disasters: an empirical study. Phys. Rev. E 75, 046109 (2007).

    Google Scholar 

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Acknowledgements

The authors acknowledge that this research was supported by the National Natural Science Foundation of China (grant number 71901156), Strategic Priority Research Program of the Chinese Academy of Sciences (grant number XDA23090502) and Fundamental Research Funds for the Central Universities. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.

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Y.M. designed the experiments, analysed the results and wrote and revised the manuscript. E.W.M.L., M.S. and R.K.K.Y. gave advice about the experimental design and data interpretation, and assisted in revising the manuscript.

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Correspondence to Yi Ma.

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Supplementary Fig. 1: Schematic of the conducted single-file crowd motion experiments under seven global densities with 10, 20, 30, 40, 50, 60 and 70 participants, where, N represents the number of experimental participants.

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Ma, Y., Lee, E.W.M., Shi, M. et al. Spontaneous synchronization of motion in pedestrian crowds of different densities. Nat Hum Behav 5, 447–457 (2021). https://doi.org/10.1038/s41562-020-00997-3

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