Phase transitions as a persistent feature of groups with leaders in models of opinion formation

A class of models of opinion formation based on the concept of cellular automata and the theory of social impact is studied, in particular the case when a strong leader and external impact are present. The rapid changes of the opinion distribution with a continuous change of a system parameter, which was previously observed for the model with geometric structure, prove to be present also for much larger class of mutual interaction architectures. We study random connections with different probability distributions. The theoretical results obtained in the framework of mean field approximation are confirmed by the numerical simulations of the model.