Kirill Kovalenko - “D-dimensional oscillators in simplicial structures“ | MoCCA’20

The talk “D-dimensional oscillators in simplicial structures“ by Kirill Kovalenko on the Moscow Conference on Combinatorics and Applications at MIPT. Annotation: Using the SIS model we will present a study about the phenomenon of localization in highly heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale of the metastable outbreaks do not show a sharp localization transition, instead there is a smooth crossover from localized to delocalized states as we approach the epidemic threshold from below. We will also show results on the same SIS model on unweighted and weighted networks. In contrast to the well-recognized point of view that diseases infect a finite fraction of vertices right above the epidemic threshold, we show that diseases can be localized on a finite number of vertices, where hubs and edges with large w