Opinion dynamics with intermittent-influence leaders on the signed social network

In this paper, the leader-follower architecture is constructed by combining intermittent-influence leaders with a signed social network. Unlike a typical network with leaders where leaders are supposed to continuously influence followers, in this article, the leaders intermittently influence followers. Furthermore, the number of influences is limited. We focus on how intermittent-influence leaders impact the evolution of followers' opinions. The relationship between followers' opinions and the number of leader broadcasts is analyzed in detail. Then, the number of broadcasts is regarded as the cost, and the changing trend of the revenue per broadcast is obtained. The results show that as the number of broadcasts increases, the revenue per broadcast decreases gradually. Finally, the concept of assimilation is introduced to weigh the costs and benefits, and the minimum number of broadcasts required for the leader to assimilate the followers is derived. Two examples are given to demonstrate the validity of the main conclusions.