2015/12/16 by Wei Su, Ge Chen, Su, Wei +3 · 5 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Optimization and Control (math.OC) #Quantum many-body systems #math.OC
paper · pdf · doi:10.48550/arxiv.1512.05058
openalex publication_date 2015/12/16 · arxiv created 2016/07/10 · arxiv updated 2016/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims at providing rigorous theoretical analysis to investigate the consensus behavior of opinion dynamics in noisy environments. It is known that the well-known Hegselmann-Krause (HK) opinion dynamics demonstrates various agreement or disagreement behaviors in the deterministic case. Here we strictly show how noises provide great help to "synchronize" the opinions of the HK model. In fact, we prove a "critical phenomena" of the noisy HK dynamics, that is, the opinions merge as a quasi-consensus in finite time in noisy environment when the noise strength is below a critical value, which implies the fragmentation phenomenon of the HK dynamics could eventually vanish in the presence of noise. On the other hand, the opinions almost surely diverge when the noise strength exceeds the critical value.