# American Institute of Mathematical Sciences

2014, 11(2): 303-315. doi: 10.3934/mbe.2014.11.303

## Local versus nonlocal barycentric interactions in 1D agent dynamics

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

Received  September 2012 Revised  March 2013 Published  October 2013

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. Mathematical Biosciences & Engineering, 2014, 11 (2) : 303-315. doi: 10.3934/mbe.2014.11.303
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