  In opinion dynamics, how to model the enduring fragmentation phenomenon
(disagreement, cleavage, and polarization) of social opinions has long
possessed a central position. It is widely known that the confidence-based
opinion dynamics provide an acceptant mechanism to produce fragmentation
phenomenon. In this study, taking the famous confidence-based Hegselmann-Krause
(HK) model, we examine the robustness of the fragmentation coming from HK
dynamics and its variations with prejudiced and stubborn agents against random
noise. Prior to possible insightful explanations, the theoretical results in
this paper explicitly reveal that the well-appearing fragmentation of HK
dynamics and its homogeneous variations finally vanishes in the presence of
arbitrarily tiny noise, while only the HK model with heterogenous prejudices
displays a solid cleavage in noisy environment.
