Article ID Journal Published Year Pages File Type
1708882 Applied Mathematics Letters 2012 5 Pages PDF
Abstract

We consider the continuous version of the Vicsek model with noise, proposed as a model for collective behaviour of individuals with a fixed speed. We rigorously derive the kinetic mean-field partial differential equation satisfied when the number NN of particles tends to infinity, quantifying the convergence of the law of one particle to the solution of the PDE. For this we adapt a classical coupling argument to the present case in which both the particle system and the PDE are defined on a surface rather than on the whole space RdRd. As part of the study we give existence and uniqueness results for both the particle system and the PDE.

Related Topics
Physical Sciences and Engineering Engineering Computational Mechanics
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