Kinetic Description of Social Dynamics: From Consensus to Flocking

Different types of phase transition for a simple model of alignment of oriented particles.

Amic Frouvelle

University Paris-Dauphine


We consider a class of models describing alignment for self-propelled particles, where a particle’s orientation continuously relaxes to the mean orientation of its neighbors . The rate of this relaxation is a given function of the norm of the local average momentum of the neighbors, and the orientation is subject to angular diffusion. The case where the rate is constant corresponds to a model of Degond & Motsch, and the case where this function is linear has been studied in detail with Degond and Liu. In this last case there is a phenomenon of phase transition. I will present here the different types of phase transitions that one can observe when the rate of relaxation is an arbitrary function, focusing on the spatial homogeneous case.
This is a joint work with Pierre Degond and Jian-Guo Liu.