Title: Collective dynamics: modeling, analysis and simulations
Speaker: Marie-Therese Wolfram (Senior Research Scientist, Radon Institute for Computational and Applied Mathematics)
Hosted by Alethea Barbaro
Abstract: Collective dynamics refer to the coordinated behavior of large groups of individuals. They can be observed in animal groups, pedestrian crowds or opinion formation processes. In all these situations the synchronization of individual characteristics emerges from complex interactions of individuals with themselves as well as their environment. Two factors are mainly responsible for these complex phenomena – social interactions and external stimuli. Synchronization of movement, also known as velocity alignment is among the most prominent examples. It is of fundamental importance in nature since it enhances the group performance in terms of survival (for example in animal groups such as fish schools).
In this talk we present different mathematical models to describe collective dynamics – ranging from biological applications to pedestrian motion. We start with the microscopic description and present the corresponding macroscopic equations. A main focus of the talk lies on segregation and alignment phenomena. We discuss the existence of such solutions on the PDE level and illustrate the behavior of the models with numerical simulations.