Opinion dynamics with the increasing peer pressure and prejudice on the signed graph

In this paper, we propose the opinion dynamics model with the increasing peer pressure and the stubborn agents. Cooperation and competition between individuals are considered simultaneously in a social network. Similar to the signed DeGroot model, we adopt a weighted average update rule in our model. We derive conditions under which opinions converge to a fixed opinion distribution. In particular, we find conditions under which opinions reach consensus or polarization (bipartite consensus). Two examples are provided to illustrate the effectiveness of the obtained results.