On Opinion Dynamics in Heterogeneous Networks

This paper studies the opinion dynamics model recently introduced by Hegselmann and Krause: (1) each agent in a group mantains a real number describing its opinion, (2) each agent updates its opinion by averaging all other opinions that are within some given confidence bounds. The confidence bounds are distinct for each agent; this heterogeneity and state-dependent topology leads to poorly-understood complex dynamic behavior. We classify the agents via the condensation digraph of their interconnection topology and, accordingly, study the spectral properties of various weakly and strongly connected components. We conjecture that all trajectories of this heterogeneous model have the following property: after finite time the state-dependent interconnection topology becomes constant. We derive novel sufficient conditions to establish this "constant-topology in finite time" conjecture and we study its implications in terms of convergence properties.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Anahita Mirtabatabaei, Francesco Bullo
• Keywords: Complex Dynamic Behavior, CORR 2010, Education, Finite Time, Interconnection Topology