Ding Fangyikuang, Li Yang, Ding Kejian
Department of Sociology, East China University of Science and Technology, Shanghai 200030, China.
School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China.
Entropy (Basel). 2023 Aug 16;25(8):1219. doi: 10.3390/e25081219.
Due to the development of social media, the mechanisms underlying consensus and chaos in opinion dynamics have become open questions and have been extensively researched in disciplines such as sociology, statistical physics, and nonlinear mathematics. In this regard, our paper establishes a general model of opinion evolution based on micro-mechanisms such as bounded confidence, out-group pressure, and in-group cohesion. Several core conclusions are derived through theorems and simulation results in the model: (1) assimilation and high reachability in social networks lead to global consensus; (2) assimilation and low reachability result in local consensus; (3) exclusion and high reachability cause chaos; and (4) a strong "cocoon room effect" can sustain the existence of local consensus. These conclusions collectively form the "ideal synchronization theory", which also includes findings related to convergence rates, consensus bifurcation, and other exploratory conclusions. Additionally, to address questions about consensus and chaos, we develop a series of mathematical and statistical methods, including the "energy decrease method", the "cross-d search method", and the statistical test method for the dynamical models, contributing to a broader understanding of stochastic dynamics.
由于社交媒体的发展，意见动态中共识和混沌的潜在机制已成为开放性问题，并在社会学、统计物理学和非线性数学等学科中得到了广泛研究。在这方面，我们的论文基于有界置信、群体外压力和群体内凝聚等微观机制建立了一个意见演化的通用模型。通过该模型中的定理和模拟结果得出了几个核心结论：（1）社交网络中的同化和高可达性导致全局共识；（2）同化和低可达性导致局部共识；（3）排斥和高可达性导致混沌；（4）强烈的“茧房效应”可以维持局部共识的存在。这些结论共同构成了“理想同步理论”，其中还包括与收敛速度、共识分岔等相关的探索性结论。此外，为了解决关于共识和混沌的问题，我们开发了一系列数学和统计方法，包括“能量递减法”、“交叉d搜索法”以及动态模型的统计检验方法，有助于更广泛地理解随机动力学。
