Stefano Boccaletti - "Synchronization in complex networks, hypergraphs and simplicial complexes" скачать в хорошем качестве

Stefano Boccaletti - "Synchronization in complex networks, hypergraphs and simplicial complexes"

The talk "Synchronization in complex networks, hypergraphs and simplicial complexes" by Stefano Boccaletti on the Moscow Conference on Combinatorics and Applications at MIPT. Annotation: All interesting and fascinating collective properties of a complex system arise from the intricate way in which its components interact. Various systems in physics, biology, social sciences and engineering have been successfully modelled as networks of coupled dynamical systems, where the graph links stand for pairwise interactions. This is, however, too strong a 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. I will discuss a general framework that allows to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. Namely, I will consider an ensemble of identical dynamical systems, organized on the nodes of a simplicial complex, and interacting through synchronization-non-invasive coupling function. The simplicial complex can be of any dimension, meaning that it can account, at the same time, for pairwise interactions (networks), three-body interactions and so on. In such a broad context, complete synchronization, a circumstance where all the dynamical units arrange their evolution in unison, exists as an invariant solution, and I will describe the necessary condition for it to be observed as a stable state in terms ofa Master Stability Function. This generalizes the existing results valid for pairwise interactions (i.e. graphs) to the case of complex systems with the most general possible architecture. The full schedule of the conference - http://mipt2020.combgeo.org/schedule/