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 N 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 Rd. As part of the study we give existence and uniqueness results for both the particle system and the PDE. © 2011 Elsevier Ltd. All rights reserved.
|Journal||Applied Mathematics Letters|
|Publication status||Published - 1 Jan 2012|
- Collective behaviour
- Interacting particle systems
- Mean-field limit
- Vicsek model