Noise-based synchronization of bounded confidence opinion dynamics in heterogeneous time-varying communication networks

Abstract

A fundamental question that arises in the analysis of the noise-based synchronization of opinion dynamics with bounded confidence (BC) is what opinion structures can be synchronized by noise. In the standard Hegselmann-Krause (HK) model, each agent examines the opinion values of all other agents and then selects neighbors who are appropriate for opinion updating in accordance with the BC scheme. In reality, however, people are more likely to exchange opinions with only a limited set of individuals, resulting in a predetermined local communication network as postulated in the DeGroot model. In this paper, we develop a new model of opinion formation that endows the heterogeneous HK dynamics with a time-varying communication topology, and we investigate its noise-induced synchronization both mathematically and numerically. We show that opinion dynamics in this model are noise-synchronizable if and only if the switching communication graph is uniformly jointly connected. Our rigorous mathematical analysis and simulation experiments demonstrate that connected discourse topology in combination with fair amounts of noise can lead to a quasi-consensus that is inducible from any initial state or any underlying system size. Our findings have profound implications for the design of future strategies of social control and global opinion optimization.