We consider self-organizing systems, i.e. systems consisting of a large number of interacting entities which spontaneously coordinate and achieve a collective dynamics. Sush systems are ubiquitous in nature (flocks of birds, herds of sheep, crowds, ...). Their mathematical modeling poses a number of fascinating questions such as finding the conditions for the emergence of collective motion. In this talk, we will consider a simplified model first proposed by Vicsek and co-authors and consisting of self-propelled particles interacting through local alignment.
We will rigorously study the multiplicity and stability of its equilibria through kinetic theory methods. We will illustrate our findings by numerical simulations.
- Partial Differential Equations Seminar