Noise, bifurcations, and modeling of interacting particle systems

Luis Mier-Y-Teran-Romero, Eric Forgoston, Ira B. Schwartz

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

    9 Scopus citations

    Abstract

    We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete bifurcation unfolds in the presence of communication delay and coupling amplitude. Relative to the center of mass, the patterns can then be described as transitions between translation, rotation about a stationary point, or a rotating swarm, where the center of mass undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of some of the stochastic patterns will be given for large numbers of particles.

    Original languageEnglish
    Title of host publicationIROS'11 - 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems
    Subtitle of host publicationCelebrating 50 Years of Robotics
    Pages3905-3910
    Number of pages6
    DOIs
    StatePublished - 2011
    Event2011 IEEE/RSJ International Conference on Intelligent Robots and Systems: Celebrating 50 Years of Robotics, IROS'11 - San Francisco, CA, United States
    Duration: 25 Sep 201130 Sep 2011

    Publication series

    NameIEEE International Conference on Intelligent Robots and Systems

    Other

    Other2011 IEEE/RSJ International Conference on Intelligent Robots and Systems: Celebrating 50 Years of Robotics, IROS'11
    Country/TerritoryUnited States
    CitySan Francisco, CA
    Period25/09/1130/09/11

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