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Kinetic hierarchy and propagation of chaos in biological swarm models

Journal article
Authors E. Carlen
R. Chatelin
P. Degond
Bernt Wennberg
Published in Physica D-Nonlinear Phenomena
Volume 260
Pages 90-111
ISSN 0167-2789
Publication year 2013
Published at Department of Mathematical Sciences, Mathematics
Pages 90-111
Language en
Links dx.doi.org/10.1016/j.physd.2012.05....
Keywords Master equation, Kinetic equations, Propagation of chaos, BBGKY hierarchy; Swarms, Correlation
Subject categories Mathematics

Abstract

We consider two models of biological swarm behavior. In these models, pairs of particles interact to adjust their velocities one to each other. In the first process, called 'BDG', they join their average velocity up to some noise. In the second process, called 'CL', one of the two particles tries to join the other one's velocity. This paper establishes the master equations and BBGKY hierarchies of these two processes. It investigates the infinite particle limit of the hierarchies at large time scales. It shows that the resulting kinetic hierarchy for the CL process does not satisfy propagation of chaos. Numerical simulations indicate that the BDG process has similar behavior to the CL process. (c) 2012 Elsevier B.V. All rights reserved.

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