Multi-dimensional Hegselmann-Krause dynamics

Abstract — We consider multi-dimensional Hegselmann-Krause model for opinion dynamics in discrete-time for a set of homogeneous agents. Using dynamic system point of view, we investigate stability properties of the dynamics and show its finite time convergence. The novelty of this work lies in the use of dynamic system approach and the development of Lyapunov-type tools for the analysis of the Hegselmann-Krause model. Furthermore, some new insights and results are provided. The results are valid for any norm that is used to define the neighbor sets. I