宁夏大学学报（自然科学版中英文）2026，Vol.47Issue(3)：225-239,15.DOI:10.20176/j.cnki.nxdz.20260504
层级社交网络中对立观点的竞争传播
Opinion Dynamics and Competition Under Social Network With Hierarchical Structures
摘要
Abstract
This study addresses the competitive propagation of opposing opinions and the formation of consen-sus in hierarchical social networks by constructing a discrete-time opinion dynamics model based on the mean-field approximation.Initially,in a strongly connected directed network,two distinct phases of opinion propaga-tion are modeled:during the early stage,individuals who have not encountered any opinions are introduced,lead-ing to the development of a three-state propagation dynamics model;in the later stage,as opinions become fully disseminated,the model simplifies to a two-state competitive propagation model.Theoretical analysis confirms the well-posedness of the model and,using Lyapunov stability theory and nonnegative matrix theory,derives suf-ficient conditions for achieving the"winner-takes-all"effect for a single opinion.Furthermore,the foundational model is expanded to include a two-layer network featuring unidirectional cross-layer influences from the deci-sion layer to the subordinate layer.The analysis reveals that the successful attainment of the"winner-takes-all"effect for a specific opinion is jointly determined by the opinion inclination of the decision layer,the internal con-nection structure of the subordinate layer,and the intensity of cross-layer influence.Notably,when there is a discrepancy between the inherent opinion inclinations of the decision and subordinate layers,if the norm of the cross-layer influence matrix exceeds a critical threshold,the dominant opinion from the decision layer can com-pletely overturn the original opinion bias of the subordinate layer,culminating in a global"winner-takes-all"sce-nario across the entire network.Numerical simulations substantiate the validity of the theoretical conditions and the effectiveness of the model,indicating that appropriate regulation of inter-layer influence can effectively steer public opinion in the desired direction.关键词
观点动力学/非线性系统/层级网络/竞争传播/李雅普诺夫稳定性理论Key words
opinion dynamics/nonlinear system/hierarchical networks/competing opinions(competitive com-munication)/Lyapunov stability theory分类
数理科学引用本文复制引用
马艳,陈志为,马婧瑛,马劲辕..层级社交网络中对立观点的竞争传播[J].宁夏大学学报（自然科学版中英文）,2026,47(3):225-239,15.基金项目
国家自然科学基金资助项目(61963032) （61963032）
银川市科技创新领军人才培养项目(2023LJRC04) （2023LJRC04）
2024年宁夏博士创新站项目资助 （）
宁夏自然科学基金资助项目(2021AAC03004) （2021AAC03004）
