Analysis of opinion consensus and fluctuation over networks

The dynamics of opinion formation with two types of individuals over social networks is analyzed in this paper. During each interaction, individuals pick up one of his neighbors with a probability depending on the neighbor's closeness and popularity and update their opinion based on the convex combination of the opinion of the interactive individuals. It is found that when the stubborn individuals have the same initial opinion, the whole population will definitely converge to a consensus, otherwise, opinion fluctuation can be be observed if regular individuals can reach at least two stubborn individuals with different opinion. Moreover, in the small world network larger average degree and rewiring probability can accelerate convergence speed to a large extent especially when they are relative small. The results may have some insight on the opinion dynamics in the real world.