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Opinion evolution of a social group with extreme opinion leaders

Opinion dynamics is a collective decision making and focuses on the study of evolution and formation of opinions in a social group. Bounded confidence rule is one of intrinsical interaction principles in the human behavior dynamics. When there is no opinion leader in a social group, for a bounded confidence based opinion dynamics, the evolution of the collective opinion of the group generally depends on the initial opinions, the confidence levels, and the group size. In this paper, a new opinion dynamics model is built, on the basis of the bounded confidence rule, to consider the opinion formation in a community with extreme opinion leaders. The leaders are divided into two classes: positive leaders and negative leaders. All the agents are assumed to have heterogeneous confidence levels. Then the impacts of the opinion leaders on the final opinions of the social agents are analyzed for different trust degree and bounded confidence levels. Finally, some computer simulation results are presented to demonstrate the formation of the collective opinion.