Georgia Institute of Technology College of Sciences

Self-organized behaviors are very common in nature and human societies: flock of birds, school of fishes, colony of bacteria, and even group of people's opinions. There are many successful mathematical models which capture the large scale phenomenon under simple interaction rules in small scale. In this talk, I will present several models on self-organized dynamics, in different scales: from agent-based models, through kinetic descriptions, to various types of hydrodynamic systems. I will discuss some recent results on these systems including existence of solutions, large time behaviors, connections between different scales, and numerical implementations.