Talk: Reluctant synchrony breaking in hypernetworks

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. The collective higher order interaction structure can be encoded by means of a hypergraph or hypernetwork. This talk will focus on dynamics of such hypernetworks. We define a class of maps that respects the higher order interaction structure, so-called admissible maps, and investigate how robust patterns of synchrony can be classified. Interestingly, these are only defined by higher degree polynomial admissible maps. This is in stark contrast to classical diadic networks where robust synchrony is governed by the linear admissible maps. Therefore, cluster synchronization on hypernetworks is truely a higher order, i.e., nonlinear effect. This observation has dramatic implications for the dynamics causing “reluctant synchrony breaking’’ when bifurcating solutions lie close to a non-robust synchrony space. The goal of this talk is to elucidate this staggering phenomenon.

Sören von der Gracht

PostDoc in Dynamical Systems

Research in network dynamical systems and its applications.