Luca Gallo (University of Catania (Italy) & Université de Namur)

Title: Stability of synchronization in simplicial complexes

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, a too strong limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. In this seminar I discuss the phenomenon of synchronization in higher-order networks. I describe a framework to study coupled dynamical systems accounting for the structure of their interactions at different orders. I show when complete synchronization exists and give the necessary condition for it to be observed as a stable state. Moreover, I consider the cases for which such a necessary condition takes the form of a Master Stability Function, thus generalizing the results valid for pairwise interactions to the case of simplicial complexes.

The seminar will take place in Room S08, Science Building (Rue Grafé 2)