Talk: Heteroclinic dynamics in network dynamical systems with higher-order interactions

Abstract

Interconnected real-world systems oftentimes contain non-pairwise interactions between agents referred to as higher order interactions. Countless works in recent years have highlighted how this structural feature crucially shapes the collective behavior. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions. In particular, we investigate under which conditions two well-known heteroclinic constructions can be realized in a corresponding network dynamical system. We find that commonly analysed model equations such as network dynamics on undirected hypergraphs induce homogeneity in the equations of motion which give rise to obstructions to the design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.

Sören von der Gracht

PostDoc in Dynamical Systems

Research in network dynamical systems and its applications.