Emergence of abstaining in Glauber opinion dynamics

We study the evolution of Glauber opinion dynamics with abstaining and tunable threshold on random graphs. The phase diagram shows plentiful features in the space of the two parameters of the model, the threshold and the abstaining probability. It is found that the threshold that limits the agents to be stable plays an important role in the emerging of abstaining in a wide spread. And it can be obtained that the observables stay the same in frozen state whatever the initial density of 0 is. We also use the mean field calculations to verify the fact of linearity between the density of 0 and the abstaining probability.