Opinion Dynamics Driven Under Leadership in Cooperation-Competition Social Networks

Social psychological research shows that although the opinions of most agents (followers) tend to prevail, sometimes a firm and influential agent (leader) can influence or even overturn the followers' preferences. Inspired by this fact, this paper designs a Degreet-model-based opinion evolution rule in cooperation-competition social networks, and uses the relevant properties of the super-stochastic matrix to conduct theoretical analysis on how the leader influence the formation of followers' opinions. Finally, algebraic conditions for achieving leader-driven opinion consensus and opinion polarization are established, respectively. Moreover, the correctness of the theoretical results is verified by numerical simulations.