Modelling Non-Linear Consensus Dynamics on Hypergraphs

OPUS 4 (Zuse Institute Berlin)

Abstract

The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models, including hypergraphs. In this paper, we explore the non-linear dynamics of consensus on hypergraphs, allowing for interactions within hyperedges of any cardinality. After discussing the different ways in which non-linearities can be incorporated in the dynamical model, building on different sociological theories, we explore its mathematical properties and perform simulations to investigate them numerically. After focussing on synthetic hypergraphs, namely on block hypergraphs, we investigate the dynamics on real-world structures, and explore in detail the role of involvement and stubbornness on polarisation.

Authors 3

1. Rohit Sahasrabuddhe

   Indian Institute of Science Education and Research Pune

   Affiliation as printed

   Indian Institute of Science Education and Research, Pune, India

2. Leonie Neuhäuser Aachen

   RWTH Aachen University · Hertie School

   Affiliation as printed

   Hertie School Data Science Lab, Berlin, Germany

   RWTH Aachen University, Germany

3. Renaud Lambiotte corresponding Aachen

   RWTH Aachen University · University of Oxford

   Affiliation as printed

   Mathematical Institute, University of Oxford, United Kingdom

   RWTH Aachen University, Germany