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Spontaneous synchronization of motion in pedestrian crowds of different densities


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 (

Code availability

The custom code used is available in an online repository (


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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.

Author information




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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Peer review information Primary handling editor: Jamie Horder.

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Supplementary Information

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).

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