Speaker
Description
Collective behaviour plays a central role in many biological, physical and social systems including neuronal activity, swarming animals, opinion formation or power grids. A common modelling approach consists in describing these situations by large interacting particle systems. Moreover, many systems exhibit an underlying network structure which describes the coupling between the particles and the corresponding strength. Often, this network structure is not fixed for all time but also evolves dynamically together with the particle system.
This talk addresses such adaptively coupled interacting systems in the large particle limit. More precisely, we start with a system of finitely many particles which is coupled to an evolution equation for the underlying network. Relying on the concept of graph convergence, we derive a limiting equation for the particles' empirical measure when their number converges to infinity. This approach will lead to consider generalised particle systems with non-locality in time (memory) and non-linear network dependence.