Asymptotic analysis of the Friedkin-Johnsen model when the matrix of the susceptibility weights approaches the identity matrix

In this paper we analyze the Friedkin-Johnsen model of opinions when the coefficients weighting the agent susceptibilities to interpersonal influence approach 1. We will show that in this case, under suitable assumptions, the model converges to a quasi-consensus condition among the agents. In general the achieved consensus value will be different from the one obtained by the corresponding DeGroot model.