Research on the Evolution of Social Power of Stubborn Individuals under the Continuous Influence of Centralized Media in Social Networks

This paper investigates the social power evolution problem within a social network composed of a centralized media and multiple stubborn individuals. In the framework, the centralized media influences the evolution of individual opinions through broadcasting. Specifically, the opinion evolution of stubborn individuals is not only affected by the centralized media but also jointly influenced by their neighbors’ opinions and their initial opinions. By integrating the reflected appraisal mechanism, this study establishes a dynamic model for social power that encompasses centralized media and examines the existence, uniqueness, and convergence of balanced social power. Furthermore, under certain specific network topologies, the relationship between the balanced social power of two stubborn individuals and their susceptibility and centralization parameters is analyzed in detail. Finally, the correctness of the relevant theoretical results is verified through numerical simulations.