Equation-free detection and continuation of a Hopf bifurcation point in a particle model of pedestrian flow

Publication: Research - peer-reviewJournal article – Annual report year: 2012



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Using an equation-free analysis approach we identify a Hopf bifurcation point and perform a twoparameter continuation of the Hopf point for the macroscopic dynamical behavior of an interacting particle model. Due to the nature of systems with a moderate number of particles and noise, the quality of the available numerical information requires the use of very robust numerical algorithms for each of the building blocks of the equation-free methodology. As an example, we consider a particle model of a crowd of pedestrians where particles interact through pairwise social forces. The pedestrians move along a corridor where they are constrained by the walls of the corridor, and two crowds are aiming, from opposite directions, to pass through a narrowing doorway perpendicular to the corridor. We focus our investigation on the collective behavior of the model. As the width of the doorway is increased, we observe an onset of oscillations of the net pedestrian flux through the doorway, described by a Hopf bifurcation. An equation-free continuation of the Hopf point in the two parameters, door width and ratio of the pedestrian velocities of the two crowds, is performed. © 2012 Society for Industrial and Applied Mathematics.
Original languageEnglish
JournalS I A M Journal on Applied Dynamical Systems
Issue number3
Pages (from-to)1007-1032
StatePublished - 2012
CitationsWeb of Science® Times Cited: 13


  • Algorithms, Doors, Pattern matching, Hopf bifurcation
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