Abstract:
Many species of animals prefer to travel in large groups such as schools of fish, flocks of birds, and herds of land animals. But how do they come to form such groups, and how can these groups be described mathematically? Similarly to gas dynamics, behavior can be considered at three different levels of abstraction: the microscopic scale, where every animal is modeled individually, the mesoscopic scale, where the distribution of animals is taken over space and velocity, and the macroscopic scale, where the distribution is only spatial. In this talk, I will begin by giving examples of particle models for socially interacting animals such as birds and fish. I will then discuss associated PDE models and our recent work on the (formal) passage from the mesoscopic to macroscopic scale. |