Opinion Dynamics of Social Networks With Intermittent-Influence Leaders

Abstract

This article constructs a leader–follower architecture by introducing intermittent-influence opinion leaders to the DeGroot model and analyzes the influence of this type of leaders on the evolution of opinions. Different from the existing studies where the leaders can convey their opinions to the followers uninterruptedly, the leaders in this article can only convey its opinion by broadcasting at some intermittent moments. First, we analyze the relationship between the leaders’ broadcast moments and the consensus opinion of followers and explain that the marginal revenue of the broadcasts is diminishing. Second, we describe the connotation of assimilation and calculate the minimum number of broadcasts required for the leaders to assimilate the followers’ opinions. Finally, aiming to make the consensus opinion of the followers and the leaders’ as close as possible, we give an optimal strategy on how to select followers to broadcast. The correctness of theoretical results is verified by numerical simulations.