层级社交网络中对立观点的竞争传播OA

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.