Local versus nonlocal barycentric interactions in 1D agent dynamics.
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.
Ecole Polytechnique Federale de Lausanne, STI-IMT-LPM, Station 17, CH-1015 Lausanne, Switzerland. max.hongler@epfl.ch.
Max-Olivier
MO
Hongler
Roger
R
Filliger
Olivier
O
Gallay
D025041:Animal Migration; D000818:Animals; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D011157:Population Dynamics