Control of kinetic opinion dynamics in popularity-adaptive social networks

Abstract: This paper presents a mathematical model for opinion dynamics in popularity-adaptive social networks, where both opinion spreading and the evolution of social media contacts depend on agents' popularity and the prominence of their views. While previous approaches accounted for the influence of popularity on opinion dynamics, we introduce a novel feedback mechanism in which opinion affects the formation of contacts. Within a kinetic modeling framework, we describe the evolution of the coupled dynamics of opinions and network structure, incorporating a class of control laws in order to promote interactions with popular individuals and amplify dominant opinions. Such control strategies are introduced to influence both opinion formation and connectivity, representing interventions such as awareness campaigns or moderation policies. Numerical results show how control strategies can mitigate polarization, foster consensus, or guide opinion distributions in dynamically evolving networks.