带有私人和表达观念的观念动力学模型分析  

An Analysis of Opinion Dynamics Models with Private and Expressed Opinions

作　　者：朱一新 何广[1] 吴艳蕾[1] ZHU Yi-xin;HE Guang;WU Yan-lei(School of Mathmatics,Physics and Finance,Anhui Polytechnic University,Wuhu 241000,China)

机构地区：[1]安徽工程大学数理与金融学院,安徽芜湖241000

出　　处：《安徽师范大学学报（自然科学版）》2024年第3期211-216,共6页Journal of Anhui Normal University(Natural Science)

基　　金：国家自然科学基金项目(62273004);安徽省高校自然科学研究基金(KJ2021A0513)。

摘　　要：研究了一类带有私人观念和表达观念的观念动力学模型的动力学特征。利用矩阵分析的相关理论,得到了系统收敛的若干结果。研究表明,当社会网络强连通时,私人观念和表达观念总是能快速收敛到一个稳定的状态,但稳态处的私人观念和表达观念仅依赖于初始的私人观念,与此同时,初始的表达观念在演化的过程中被遗忘。如果社会网络中不存在执拗个体,个体的观念将达到一致。观念在稳态处的分歧程度也被详细地分析,在一些特殊的条件下,可以通过表达观念的分歧程度来估计私人观念的分歧程度。最后我们利用数值仿真对所得结果进行了验证。In this paper,an opinion dynamics model with private and expressed opinions is analyzed.By utilizing the relevant theories of matrix analysis,the conditions of system convergence are obtained.It has been found that when social networks are strongly connected,private and expressed opinions always converge quickly to steady opinions.At the same time,the steady opinions only depends on initial private opinions,while initial expressed opinions are forgotten in the process of evolution.If there are no stubborn individuals in the social network,opin-ions will reach a consensus.The disagreement level at steady opinions is also analyzed,and under some special conditions,the disagreement level of private opinions can be estimated by the disagreement level of expressed opinions.Finally,a numerical simulation example is used to prove this result.

关 键 词：观念动力学 私人观念和表达观念 收敛 一致 

分 类 号：O193[理学—数学]