Chapter

Mathematical Modeling of Collective Behavior in Socio-Economic and Life Sciences

Part of the series Modeling and Simulation in Science, Engineering and Technology pp 297-336

Date:

Particle, kinetic, and hydrodynamic models of swarming

  • José A. CarrilloAffiliated withICREA - Departament de Matemàtiques, Universitat Autònoma de Barcelona Email author 
  • , Massimo FornasierAffiliated withJohann Radon Institute for Computational and Applied Mathematics (RICAM)
  • , Giuseppe ToscaniAffiliated withDepartment of Mathematics, University of Pavia
  • , Francesco VecilAffiliated withJohann Radon Institute for Computational and Applied Mathematics (RICAM)

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Summary

We review the state-of-the-art in the modelling of the aggregation and collective behavior of interacting agents of similar size and body type, typically called swarming. Starting with individual-based models based on “particle”-like assumptions, we connect to hydrodynamic/macroscopic descriptions of collective motion via kinetic theory. We emphasize the role of the kinetic viewpoint in the modelling, in the derivation of continuum models and in the understanding of the complex behavior of the system.