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Kinetic hierarchy and propagation of chaos in biological swarm models

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-scale. 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.
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https://hal.archives-ouvertes.fr/hal-00632623
Contributor : Pierre Degond <>
Submitted on : Friday, October 14, 2011 - 6:05:51 PM
Last modification on : Thursday, March 5, 2020 - 5:59:08 PM
Document(s) archivé(s) le : Sunday, January 15, 2012 - 2:25:17 AM

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  • HAL Id : hal-00632623, version 1

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Eric Carlen, Robin Chatelin, Pierre Degond, Bernt Wennberg. Kinetic hierarchy and propagation of chaos in biological swarm models. Physica D : Nonlinear Phenomena, Elsevier, 2013, 260, pp.90-111. ⟨hal-00632623⟩

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