Opinion Dynamics on Higher-Order Social Networks: A Continuous-Time Perspective
本文提出一个连续时间动力学模型，研究超图表示的高阶社交网络中的观点形成过程，引入扩散式交互函数刻画不同阶交互，并分析有无固执个体时的收敛与稳定性，数值实验验证了模型效果。
Opinion dynamics models that elucidate the evolution and formation of opinions conventionally focus on pairwise interactions within graphs, often overlooking the complex higher-order interactions that arise in real-world social networks, such as online meetings and group chats. In this article, a continuous-time dynamical system is developed to study opinion-forming processes over higher-order networks associated with undirected hypergraphs. The proposed model introduces a novel diffusion-like interaction function to characterize interactions of different orders over hypergraphs. The convergence and stability of the dynamical systems are further examined in both the presence and absence of stubborn individuals. Building on traditional opinion dynamics models and integrating weak-tie theory, we emphasize the critical role of higher-order interactions in shaping individual opinions, enhancing network communication efficiency, and mitigating opinion polarization. Finally, all theoretical results are extensively investigated and empirically validated through numerical experiments on both synthetic and real-world network datasets.