Transport phenomena in collective dynamics: from micro to social hydrodynamics

Metric versus topologic interactions

Pierre Degond

Imperial College London

There is increasing evidence that interactions among social agents such as birds or fish depend on topologic rather than metric proximity. In the latter case, the interaction intensity is a function of the metric distance, while in the former one, it depends on the proximity rank irrespective of the distance between the agents. Such topological interactions are scale-free and raise important questions that have been seldom addressed by mathematicians. In this talk, we will present one of the very first attempts to build kinetic models based on topological interaction rules and we will show that this results in completely new types of kinetic models which bring in important new open questions. This is a joint work with Adrien Blanchet from the Toulouse School of Economics.