The Opinion Dynamic Model With Noise

Opinion dynamic is a new research field, which computer analysis tools and mathematical-physical models are introduced to the study of opinion dynamics mechanism. It is related to the social dynamic, physics and complexity science. In the last decade, physicists have started to work actively in opinion dynamics, and many models have been designed. In this paper, based on the typical opinion model, a q-voter model with the coexistence of stubborn agents and anticonformity is discussed on a complete graph. This result shows that the anticonformity weaken the impact of the stubborn agents on the system.In the first section, several basic models in opinion dynamics are described, including the Voter model, the Sznajd model, the Majority Rule model, q-voter model and Deffuant model. The first four models are typical discrete binary-variable models, which is based on the Ising model. And the last one is continuous model with bounded confidence. Based on the models, some opinion models on complex network are discussed. In the next two sections, we focus on the model with social noise, finding that noise affects the ordering and the stable states of the system. The zealots cause the system disordered in the Voter model as well as Sznajd model. In the third section, the system with the anticonformity will reach the states with majority instead of the absolute consensus states in the Voter model and the Sznajd model. When the probability of anticonformity is greater than the threshold, the system can reach the states with majority. Otherwise there is no majority in the system. In the fourth section, we discuss a non-linear q-voter model with the coexistence of stubborn agents and anticonformity on a complete graph. We investigate the interaction between stubborn agents and the anticonformity which is tested by the majority rule to find out how the interaction between stubborn agents and the anticonformity influences the stability of the system. Both of the states with majority are possible, when the probability of anticonformity is low. But the probability that the opinion with stubborn agents is the majority is greater. It gets lower with the increasing probability of anticonfirmity.