Mean-field limit for the stochastic Vicsek model

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 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 R d . As part of the study we give existence and uniqueness results for both the particle system and the PDE.

• Publication year

  2011

• Venue

  Applied Mathematics Letters

• Publication date

  2011-02-07

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1016/j.aml.2011.09.011arXiv 1102.1325
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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