Dynamical Systems Seminar: Istvan Zoltan Kiss (Northeastern University London )

Mean-field limits of spreading dynamics on higher-order networks

Abstract: Exact analysis of spreading dynamics on networks typically requires solving systems of differential equations whose dimension grows exponentially with network size, necessitating systematic approximation methods. In this talk, I will discuss two approaches-top-down and bottom-up-for deriving mean-field limits and approximations of high-dimensional models [1]. Both approaches rely on closure assumptions, which are usually justified only for networks with strong structural properties, such as symmetry, tree-like structure, or good mixing, as in configuration-model networks. I will present two exact results: (i) for tree-like networks using the bottom-up approach [2], and (ii) for networks with Poisson-type degree distributions using the top-down approach [3]. In the second part of the talk, I will extend these mean-field approaches to higher-order networks (hypergraphs), where group interactions involving three or more nodes give rise to qualitatively new phenomena—including bistability and multistability—that are absent in classical pairwise models. I will focus on the interplay between structure and dynamics and take steps towards disentangling their respective roles in determining system-level outcomes. I will show that (i) even highly symmetric structures can support these complex behaviours [4,5], and (ii) overlap between hyperedges can inhibit bistability and fundamentally alter its emergence mechanisms [6].