Bounded confidence opinion dynamics with opinion leaders and environmental noises

Opinion dynamics is a kind of collective decision-making process and focuses on the study of evolution and formation of opinions within a human society. Particularly, bounded confidence rule is one of intrinsic interaction principles in the opinion dynamics. In this paper, a leader-follower opinion dynamics model is built, with the help of the bounded confidence rule, to consider the opinion formation of a community, which is constituted of opinion leaders and opinion followers. At the same time, environmental uncertainties are considered in the opinion formation and called as environmental noises, which are modeled as Gaussian stochastic processes. All the agents are assumed to have heterogeneous confidence levels. Then the impacts of the opinion leaders and the environmental noises on the final opinions of the opinion followers are analyzed. Finally, some simulation results are presented to demonstrate the collective opinion evolution in three cases: no opinion leader, single opinion leader and multiple opinion leaders.