Modeling and Control in Social Dynamics

Flocking dynamics in different scales

Changhui Tan

Rice University

Self-organized behavior is very common in nature and human societies. One widely discussed example is the flock formed by birds flying towards the same direction. Several models such as Cucker-Smale and Motsch-Tadmor are very successful in characterizing the flocking behavior. In this talk, we will discuss about flocking models in different scales, describing the alignment phenomenon. In particular, the macroscopic representation of the flocking models yields a very interesting fluid system: compressible Eulerian dynamics with nonlocal alignment. We show a critical threshold phenomenon for the fluid system. Under suitable initial conditions, the system has global strong solution, and it converges to a flock. On the other hand, another set of initial conditions will lead to a finite time break down of the system. We also add attraction-repulsion force to the system and study the long time behavior.