2019/12/23 by Ge Chen, Chen, Ge, Wei Su +6 · 2 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Electrical engineering #FOS: Mathematics #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Quantum many-body systems #Systems and Control (eess.SY) #cs.SY #eess.SY #electronic engineering #information engineering #math.OC
paper · pdf · doi:10.48550/arxiv.1912.10753
arxiv created 2019/12/23 · openalex publication_date 2019/12/23 · arxiv updated 2019/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Hegselmann-Krause (HK) model is a wellknown opinion dynamics, attracting a significant amount of interest from a number of fields. However, the heterogeneous HK model is difficult to analyze - even the most basic property of convergence is still open to prove. For the first time, this paper takes into consideration heterogeneous HK models with environment or communication noise. Under environment noise, it has been revealed that the heterogeneous HK model with or without global information has a phase transition for the upper limit of the maximum opinion difference, and has a critical noise amplitude depending on the minimal confidence threshold for quasi-synchronization. In addition, the convergence time to the quasi-synchronization is bounded by a negative exponential distribution. The heterogeneous HK model with global information and communication noise is also analyzed. Finally, for the basic HK model with communication noise, we show that the heterogeneous case exhibits a different behavior regarding quasi-synchronization from the homogenous case. Interestingly, raising the confidence thresholds of constituent agents may break quasi-synchronization. Our results reveal that the heterogeneity of individuals is harmful to synchronization, which may be the reason why the synchronization of opinions is hard to reach in reality, even within that of a small group.