Collective Behavior: Macroscopic versus Kinetic Descriptions

Emergence of flocking and consensus

Sébastien Motsch

Arizona State University

Flocking behavior is a spectacular and still mysterious phenomenon. From neighboring interactions emerge large scale structures. Several models have been proposed to apprehend such dynamics. For instance, the Cucker-Smale model is a popular model that generates such flocking behavior. In the first part of this talk, we propose and discuss a different dynamics that aim to address some drawbacks of the Cucker-Smale model.

In the second part, we present some recent results in opinion formation. Models of opinion formation share many similarities with flocking behavior. One of the main question is whether a dynamics will reach a 'consensus'. The additional difficulty is that the support of the influence function considered has a compact support. Thus, one has to keep track of the 'connectivity' of the graph of interaction.