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Mathematical Biosciences and Engineering

2014, Volume 11, Issue 2: 303-315. doi: 10.3934/mbe.2014.11.303
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Local versus nonlocal barycentric interactions in 1D agent dynamics

  • 1.
    Ecole Polytechnique Fédérale de Lausanne, STI-IMT-LPM, Station 17, CH-1015 Lausanne
  • 2.
    Bern University of Applied Sciences, Quellgasse 21, CH-2501 Biel
  • 3.
    IBM Zurich Research Laboratory, Saeumerstrasse 4, CH-8803 Rueschlikon
  • Published: 01 October 2013

  • MSC : Primary: 82C22, 82C23; Secondary: 92D25, 82C70.

  • The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from $(a)$ a finite extension of the agents interaction range and $(b)$ a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.

    Citation: Max-Olivier Hongler, Roger Filliger, Olivier Gallay. Local versus nonlocal barycentric interactions in 1D agent dynamics[J]. Mathematical Biosciences and Engineering, 2014, 11(2): 303-315. doi: 10.3934/mbe.2014.11.303

    Related Papers:

  • The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from $(a)$ a finite extension of the agents interaction range and $(b)$ a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.


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