Collective Dynamics

Many phenomena in daily life can be viewed as an interplay between ensembles of objects that communicate and interact in a non-local manner. Basic examples of such phenomena include flocking of birds and schooling of fish where the objects – individual birds or fish – interact with each other forming a larger ensemble.

Recently, together with P. Mucha, J. Peszek and E. Zatorska we review singular models of flocking. Starting from the microscopic Cucker-Smale model with singular communication weight, through its mesoscopic mean-field limit, up to the corresponding macroscopic regime.

Moreover, with P. Mucha and J.Peszek we introduced a novel density-induced consensus protocol where agents receive information only from sufficiently dense crowds in their immediate vicinity. We prove the basic mathematical properties of the system and concentrate on the presentation of interesting behaviors of the solutions