Heterogeneous hegselmann-krause dynamics with environment and communication noise

作     者：Chen, Ge Su, Wei Ding, Songyuan Hong, Yiguang 

作者机构：National Center for Mathematics Interdisciplinary Sciences & Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Automation and Electrical Engineering University of Science and Technology Beijing Beijing100083 China  Department of Chemistry College of Chemistry and Chemical Engineering Xiamen University Xiamen361005 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2019年

核心收录：

主　　题：Synchronization 

摘      要：The Hegselmann-Krause (HK) model is a well-known 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. Copyright © 2019, The Authors. All rights reserved.