A Mathematical Model of the Formation of Lanes in Crowds of Pedestrians Moving in Opposite Directions

<div>Evolution of the number of pedestrians moving counterclockwise minus the number of pedestrians moving clockwise in lane 1, the inner lane. In (a), we use the time <svg height="8.02022pt" id="M110" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="341" vert-adv-y="341"></glyph.data></g></svg>, but, in (b), we use the number of collisions as the independent variable.</div>

Discrete Dynamics in Nature and Society

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Figure 2

Figure 2: A Mathematical Model of the Formation of Lanes in Crowds of Pedestrians Moving in Opposite Directions 