Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution. Keywords. Flocking, nonlinear friction equations, mass transportation methods.

• Type: Journal
• Year: 2010
• Where: SIAMMA
• Authors: J. A. Carrillo, M. Fornasier, J. Rosado, G. Toscani
• Keywords: Continuous Kinetic Version, Kinetic Version, SIAMMA 2010, Solution